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SWELLING
6
Swelling 6.1 MODERN VIEWS ON KINETICS OF SWELLING OF CROSSLINKED ELASTOMERS IN SOLVENTS E. Ya. Denisyuk and V. V. Tereshatov Institute of Continuous Media Mechanics and Institute of Technical Chemistry, Ural Branch of Russian Academy of Sciences, Perm, Russia
6.1.1 INTRODUCTION Diffusion phenomena encountered in mass-transfer of low-molecular liquids play an important role in many technological processes of polymer manufacture, processing, and use of polymeric materials. Diffusion of organic solvents in crosslinked elastomers may cause considerable material swelling. In this case, the polymeric matrix experiences strains as large as several hundred percent, while a non-homogeneous distribution of a liquid caused by diffusion results in establishing stress-strain state capable of affecting the diffusion kinetics. The processes of material deformation and liquid diffusion in such systems are interrelated and nonlinear in nature and are strongly dependent on physical and geometrical nonlinearities. Therefore, exact relations of nonlinear mechanics of elasticdeformable continuum are the mainstream of a sequential theory of mass-transfer processes of low-molecular liquids in elastomers. The general principles of the development of nonlinear models of mass transfer in elastically deformed materials were developed in previous studies.1,2 The general formulation of constitutive equations and the use of non-traditional thermodynamic parameters such as partial stress tensors and diffusion forces lead to significant difficulties in attempts to apply the theory to the description of specific systems.3,4 Probably, because of this, the theory is little used for the solution of applied problems. In the paper,5 a theory for mechanical and diffusional processes in hyperelastic materials was formulated in terms of the global stress tensor and chemical potentials. The approach described in1,2 was used as the basic principle and was generalized to the case of a multi-component mixture. An important feature of the work5 is that, due to the structure of constitutive equations, the general model can be used without difficulty to describe specific systems. In the paper6 the nonlinear theory5 was applied to steady swelling processes of crosslinked elastomers in solvents. The analytical and numerical treatment reveals three possible mechano-diffusion modes which differ qualitatively. Self-similar solutions obtained for these modes describe asymptotic properties at the initial stage of swelling. These
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6.1 Modern views on kinetics of swelling of crosslinked elastomers in solvents
modes are related to thermodynamic material properties. The theoretical predictions have been verified in the experiments conducted on real elastomers. 6.1.2 FORMULATION OF SWELLING FOR A PLANE ELASTOMER LAYER Consider an infinite plane elastomer layer of thickness 2h embedded in a low-molecular liquid. Suppose that the elastomer initially does not contain liquid and it is not strained. This state is taken as a reference configuration. Let us introduce the Cartesian coordinates (x,y,z) with the origin placed in the layer center and relate them to a polymer matrix. In the examined problem, the Cartesian coordinates will be used as the material coordinates. With reference to the layer, the x axis has a transverse direction and the other axes have longitudinal directions. In our approach, we define the problem under consideration as a one-dimensional problem, in which all quantities characterizing the elastomer state depend only on the x-coordinate. On swelling, the layer experiences transversal and longitudinal deformations which can be written as X = X(x,t) Y = (t)y Z = (t)z
[6.1.1]
where (X,Y,Z) are the spatial Cartesian coordinates specifying the actual configuration of the polymeric matrix. From this it follows that the relative longitudinal stretch of the layer is 2 = 3 = t and the relative transversal stretch is 1 = x t = X x . The quantity J = 1 2 3 =
2
[6.1.2]
characterizes a local relative change in the material volume due to liquid absorption. The boundary conditions and the relations describing free swelling of the plane layer in the reference configuration are represented in5 as N N ---------1- = ------ D ---------1- N 1 = N 1 x t x x t
[6.1.3]
N 2 t = 0
[6.1.4]
1 x = 0
[6.1.5]
N 1 x 0 = 0
[6.1.6]
N 1 0 t x = 0 X 0 t = 0
[6.1.7]
h t = 0 1 h t = 0
[6.1.8]
2 x t = 3 x t = 0
[6.1.9]
where: N1,N2 μ
the molar concentrations of the liquid and the chains of polymeric network of elastomer, respectively, the chemical potential of the liquid dissolved in material
E. Ya. Denisyuk and V. V. Tereshatov k
295
(k = 1,2,3) are the principal values of the Piola stress tensors.
The angular brackets denote integration with respect to coordinate x: = h
–1
h
dx 0
Because of a symmetry of the swelling process in a layer, the problem is solved for 0
–1
[6.1.10]
where the volume fraction of the polymer is = N2 V2 N1 V1 + N2 V2
[6.1.11]
where: V1 and V2 the molar volumes of liquid and chains of the elastomer network, respectively
To make the definition of the examined problem complete, we need to add to the above model equations, the constitutive relations for mechanical stress tensor and chemical potential of a liquid. According to5,6 this the equations are given by –1
–1
–1
k = RTV 2 k – I 1 k 3 – pJ k –1 1 3
= mix + RTZ
1 3 + V1 p 2
mix = RT ln 1 – + + where: R T
the gas constant per mole the absolute temperature
[6.1.12] [6.1.13] [6.1.14]
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6.1 Modern views on kinetics of swelling of crosslinked elastomers in solvents μmix p Z
the chemical potential of mixing pressure the Flory-Huggins interaction parameter = V2/V1
I1
= 1 + 2 + 3
1
I1/J2/3
2
2
2
The above equations follow from the classical elasticity theory and the Flory theory of polymeric networks.7 From Eq. [6.1.5] and the second condition of Eq. [6.1.8], we find that 1(x,t) = 0. This equation together with Eq. [6.1.12] yields the expression for pressure. By substituting it in the formulas for chemical potential [6.1.13] and longitudinal stresses, we find, using Eqs. [6.1.2] and [6.1.10], that –1
2
5
[6.1.15]
4
[6.1.16]
2 = 3 = RTV 2 – J –1
= mix 1 J + RTZ J
A substitution of Eq. [6.1.15] in Eq. [6.1.9] gives an expression for longitudinal stretch of the layer 6
2
= J x t
[6.1.17]
With consideration of Eq. [6.1.16], the boundary condition at x = h is transformed to –1
4
mix 1 J RT + Z J = 0
[6.1.18]
Thus, the initial swelling problem for a plane layer is reduced to a boundary value problem for diffusion equation [6.1.3] with boundary conditions of Eqs. [6.1.6], [6.1.7], [6.1.17] and [6.1.18]. The solution to this problem provides a full description of swelling processes in the plane layer. In other words, using Eqs. [6.1.1], [6.1.2], [6.1.10] and [6.1.15] we can define a current distribution of a liquid through the layer and calculate the stress-strain state of the material. It should be noted that boundary conditions of Eq. [6.1.18] and Eq. [6.1.17] specify the existence of positive feedback in the system, which is responsible for the onset of unsteady boundary regime during material swelling. The nonlinear distributed systems with positive feedback are generally known as active media and are distinguished for their complex and multimode response.8 In free swelling, the response of elastomers is, in a sense, similar to that of active media. Such behavior is most pronounced when the extent of material swelling is high, which makes this case worthwhile for detailed investigation. For high-swelling elastomers, the volume fraction of polymer in equilibrium swelling state denoted in the following as and the volume fraction of polymer at the elastomer-liquid interface = 1/J entering Eq. [6.1.18] are small quantities. The asymptotic behavior of the function μ( ) at 0 is described by RT = – b
[6.1.19]
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297
The constants b and a can be calculated using the Flory equation [6.1.14]. A second order expansion of ln(1 ) as a power series of gives b = 1/2 and = 2. The scaling approach gives a slightly different value of , which is found to be = 9/4 (des Cloizeaux law9). A volume fraction of the polymer in equilibrium swelling state can be determined by substituting Eq. [6.1.19] in Eq. 6.1.18] and setting = J-1 = and -1/3, yields – 3 3 – 1 bZ . Then, using Eqs. [6.1.18], [6.1.19] and the last relation, we arrive at the following expression for the volumetric swelling ratio of the layer at the elastomer-liquid interface: –1
J
13
6d
[6.1.20]
where 2 d = --------------------3 + 1
[6.1.21]
Note that approximate Eq. [6.1.20] defines the strain dependence of the equilibrium swell ratio of the elastomer in a liquid medium under conditions of biaxial symmetric material extension. Substituting Eq. [6.1.17] in Eq. [6.1.20], we express the boundary swell ratio in terms of liquid distribution in the layer J h t =
2d – 1
2
J x t
d
[6.1.22]
Then the problem is finally defined as u t = k u I u x x ; x 0 1 , t > 0
[6.1.23]
u x 0 = 0 u x 1 t = 0
[6.1.24] 2 d
1 – u 0 t + = 1 – u x t +
[6.1.25]
Here we assign dimensions to the variables. The quantities h and h2/D0 (where D0 is the value of diffusion coefficient in the state of ultimate elastomer swelling) are used as the units of distance and time. For the sake of convenience we transform, the coordinate to x 1 – x . Integrating for x between the limits from 0 to 1 in Eq. [6.1.25] is designated by angular brackets. The function u(x, t) takes the value over the interval (0, 1) and represents a dimensionless concentration of penetrating liquid. It is related to the liquid concentration and local material swelling by the following equations: N1 = V1
–1
–1
– 1 u x t J x t = 1 – u x t +
[6.1.26]
The quantity l = represents the longitudinal layer stretch normalized to unity. By virtue of [6.1.17] and [6.1.26] we may write 6
2
I t = 1 – u x t +
[6.1.27]
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6.1 Modern views on kinetics of swelling of crosslinked elastomers in solvents
Dimensionless diffusion coefficient is defined by the formula k(u, l) = D(u, l)/D0. The longitudinal stresses in the layer (15) are expressed in terms of dimensionless stresses q(x, t) by –1
2 = 3 = RTV 2 q x t
[6.1.28]
where according to Eqs. [6.1.15] and [6.1.27] q x t =
–1 3
2
6
t 1 – 1 – u x t + I t
[6.1.29]
Consider two functions 2
g 1 t = u x t g 2 t = u x t
[6.1.30]
which are integral characteristics of swelling kinetics for a plane layer and can be determined from experiments. The first function characterizes a relative amount of liquid absorbed by a polymer in time t and the second function according to Eq. [6.1.27] is related to longitudinal layer deformation. For high-swelling elastomers 6
g2 t I t
[6.1.31]
The numerical results obtained by solving model problem of Eqs. [6.1.23] [6.1.25] for a constant diffusion coefficient are plotted in Figure 6.1.1.6 The obtained curves show the evolution of penetrating liquid concentration and longitudinal stresses. It is seen that the boundary liquid concentration during swelling monotonically increases.
Figure 6.1.1. Distribution of penetrating liquid (a) and longitudinal stresses (b) during swelling of a plane layer with constant diffusion coefficient k(u, l) = 1 at = 0.1 and d = 2/9: 1 t = 0.05; 2 t = 0.2; 3 t = 0.4; 4 t = 0.6; 5 t = 1; 6 t = 1.8. [Adapted, by permission, from E. Ya. Denisyuk, V. V. Tereshatov, Vysokomol. soed., A42, 74 (2000)].
6.1.3 DIFFUSION KINETICS OF PLANE LAYER SWELLING Consider two stages of swelling process in a plane layer the initial and final. In the initial stage, the influence of the opposite layer boundary on the swelling process is non-essential
E. Ya. Denisyuk and V. V. Tereshatov
299
and therefore diffusion in a layer of finite thickness at sufficiently small values of time can be considered as the diffusion in half-space. At the very beginning of the swelling process the amount of absorbed liquid is rather small. Hence, we may set u x t 0 in the right-hand side of Eqs. [6.1.25] and [6.1.27] which results in u 0 t 0 =
2d
– 1 – I t
13
and Eq. [6.1.23] becomes an usual parabolic equation describing diffusion on a half-line with constant boundary concentration 0. It has self-similar solution of the form u(x,t)= 0(x/t1/2). The function satisfies the equation (k()' + ' /2 = 0 and the boundary conditions 0 = 1 + = 0
[6.1.32]
From this follows the expression for the integral process characteristics g1 t = 0 M1 t
12
2
g2 t = 0 M2 t
12
where
Mp =
p
d p = 1 2
[6.1.33]
0
These relations define the asymptotic properties of swelling at t 0 . As more and more liquid is absorbed, the longitudinal strains in the layer increase. By virtue of Eq. [6.1.25], this causes the growth of liquid concentration at the boundary. For high-swelling materials at sufficiently large values of time, all terms in Eq. [6.1.25] involving as a multiplier factor can be neglected to the first approximation. The resulting expression is written as 2
u 0 t = u x t
d
[6.1.34]
where the angular brackets denote integrating for x in the limits from 0 to + . Since for arbitrary dependence of k(u,l) a boundary-value solution of equation [6.1.23] on the half-line with boundary condition of Eq. [6.1.34] cannot be represented in a similar form, we restrict our consideration to a model problem with diffusion coefficients defined by s
[6.1.35]
s 6p
[6.1.36]
k u I = u s 0 k u I = u I s 0 p 0
(Let us assume that s = 0 corresponds to a constant diffusion coefficient k(u, l) = 1). The analysis of this problem allows us to qualitatively explain many mechanisms of diffusion kinetics of elastomer swelling.
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6.1 Modern views on kinetics of swelling of crosslinked elastomers in solvents
First, consider the diffusion coefficient defined by Eq. [6.1.35]. In this case, Eq. [6.1.23] on the half-line has a variety of self-similar solutions, which can be written as u x t = t x t
[6.1.37]
where the function satisfies conditions of Eq. [6.1.32] and defines the profile of the diffusion wave, (t) describes boundary conditions and (t) function specifies the penetration depth of diffusion wave. Eq. [6.1.37] satisfies the boundary condition of Eq. [6.1.34] and Eq. [6.1.23] on the half-line with the diffusion coefficient of Eq. [6.1.35] in the following cases: 1) (t), (t) are the functions of power type (power swelling mode); 2) (t), (t) are the functions exponentially depending on time (exponential swelling mode); 3) (t) ~ (t0 t)m, (t)~(t0 - t)n, where m, n < 0 (blow-up swelling mode). Power swelling mode occurs at sufficiently small values of s. In this case, the amount of absorbed liquid, boundary concentration, the depth of diffusion wave penetration and the longitudinal layer deformation are the power function of time. If the parameter s approaches the critical value sc = 2 d – 4
[6.1.38]
Swelling process is governed by exponential law. And finally, if s > sc, the swelling mode is of a blow-up nature. The solutions describing these modes are given below. I. Power mode (s < sc): ms n
2m m
u x t = M 2 t = x M 2 t 2q – 1 q
g1 t = M1 M2
[6.1.39]
ms r
t g2 t = M2 t
[6.1.40]
1 1d–2 1d–1 1 m = ------------ n = ------------------- q = ------------------- r = -------------------sc – s sc – s sc – s d sc – s
[6.1.41]
II. Exponential mode (s = sc): 2
2
u x t = exp M 2 t – t 0 = xM 2 exp s c M 2 t – t 0 2 2
g 1 t = M 1 M 2 exp s c 2 + 1 M 2 t – t 0 2
g 2 t = exp s c 2 + 1 M 2 t – t 0 III. Blow-up mode (s > sc): 2m
ms
u x t = M 2 t 0 – t = x M 2 t 0 – t 2q – 1
g1 t = M1 M2
q
2r
t0 – t g2 t = M2 t0 – t
r
where the exponents are defined by Eqs. [6.1.41] but if s > sc, then m, n, q, r < 0.
E. Ya. Denisyuk and V. V. Tereshatov
301
For power and blow-up swelling modes, is derived from the equation s ' ' + n ' – m = 0 . For an exponential mode, this equation will be valid if we put n = sc/2 and m = 1. The constants M1 and M2 are evaluated from Eq. [6.1.33] and the constant t0 can be estimated by the order of magnitude from the condition 2d –2 u 0 t 0 0 . For the exponential mode, we have t0 ~ 2dM 2 ln , and for the – 2 2d m blow-up mode, t0 ~ M 2 . It is worth noting that at m = 1/s, which holds only if s = 1/d 2, solution of Eq. [6.1.39] is expressed in terms of primary functions and describes the diffusion wave propagating with a constant velocity d: u x t = 1 – 2d
1s
dt – x
1s
The solution describing the blow-up mode turns into infinity at the finite time. In the global sense the boundary-value problems admitting such solutions are time unsolvable and are generally applied to modeling high rate physical-chemical processes.10 It is quite evident that all solutions to the swelling problem for a layer of finite thick are limited and each of the self-similar solutions presented in this study describes asymptotic properties of diffusion modes at initial well-developed stage of swelling. At the final swelling stage u x t 1 , an approximate solution to the problem can be obtained by its linearization in the vicinity of equilibrium u = 1. To this end, one needs to introduce a variable v(x, t) = 1 u(x, t). After transformation we get v t = v xx v x 1 t = 0 v 0 t = 2d v x t By making use of the method of variable separation, we find v x t =
2
ak exp –k t cos k 1 – x
[6.1.42]
k=1
where the values of k are determined from the equation k = 2d tan k
[6.1.43]
Restricting ourselves to the first term of a series Eq. [6.1.42], we can write for the final swelling stage the equation of kinetic curve 2
g 1 t = 1 – a 1 1 exp – 1 t sin k
[6.1.44]
The above expressions allow us to describe the shape of kinetic curves g1(t) in general terms. In particular, as it follows from Eqs. [6.1.39] [6.1.41] at q < 1, the kinetic curves in the coordinates (t,g1) are upward convex and have the shape typical for pseudonormal sorption. This takes place at s < sc/2 1. If s = sc/2 1, then q = 1, which corresponds to a linear mode of liquid absorption. At s > sc/2 1 the lower part of the kinetic curve is convex in a downward direction and the whole curve becomes S-shaped. Note that in terms of coordinates (t1/2,g1) at s 0 all the kinetic curves are S-shaped. Hence, the
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6.1 Modern views on kinetics of swelling of crosslinked elastomers in solvents
Figure 6.1.2. Diffusion kinetics of plane layer swelling for diffusion coefficient k(u) = us at = 0.1 and d = 2/9; a, b are power swelling modes at s = 1 and s = 2.5, respectively; c exponential swelling mode (s = 5); d blow-up swelling mode (s = 5.5). Numerals over curves denote correspond to instants of time. [Adapted, by permission, from E. Ya. Denisyuk, V. V. Tereshatov, Vysokomol. soed., A42, 74 (2000)].
obtained solutions enable us to describe different anomalies of sorption kinetics observed in the experiments on elastomer swelling in low-molecular liquids. Figure 6.1.26 gives the results of numerical solution to problems of Eq. [6.1.25] with diffusion coefficient defined by Eq. [6.1.35]. The kinetic curves of swelling at different values of s are depicted in Figure 6.1.3.6 Here it can be noted that strain dependence of the diffusion coefficient described by Eq. [6.1.36] does not initiate new diffusion modes. The obtained three self-similar solu-
E. Ya. Denisyuk and V. V. Tereshatov
303
Figure 6.1.3. Kinetic curves of plane layer swelling at different values of concentration dependence of diffusion coefficient ( = 0.1,d = 2/9): a power law mode (1 s = 0; 2 s = 1; 3 s = 1.5; 4 s = 2.5); b exponential (5 s = 5) and blow-up mode (6 s = 5.5). [Adapted, by permission, from E. Ya. Denisyuk, V. V. Tereshatov, Vysokomol. soed., A42, 74 (2000)].
tions hold true. Only critical value sc is variable and it is defined by expression s c = 2 – p d – 4 . This fact can be supported by a direct check of the solutions. 6.1.4 EXPERIMENTAL STUDY OF ELASTOMER SWELLING KINETICS The obtained solutions can be applied to experimental study of the diffusive and thermodynamic properties of elastomers. In particular, with the relation s = 2 d – 4 – 1 d – 1 q
[6.1.45]
following from Eqs. [6.1.38] and [6.1.41] we can estimate the concentration dependence of the diffusion coefficient of a liquid fraction in elastomer. According to Eq. [6.1.40] the parameter q is determined from the initial section of the kinetic swelling curve. Experimental estimates of the parameter r can be obtained from the strain curve l(t) using Eqs. [6.1.31] and [6.1.40]. Then by making use of the formula d =1 q/r
[6.1.46]
following from Eq. [6.1.41] we can evaluate the parameter d which characterizes the strain dependence of the equilibrium swelling ratio of elastomer under symmetric biaxial extension in Eq. [6.1.45]. Generally the estimation of this parameter in tests on equilibrium swelling of strained specimens proves to be a tedious experimental procedure. The value of diffusion coefficient in an equilibrium swelling state can be determined from the final section of kinetic swelling curve using Eq. [6.1.44], which is expressed in terms of dimensional variables as 2
2
g 1 t = 1 – C exp – 1 D 0 t h
[6.1.47]
where 1 is calculated from Eq. [6.1.43). For d = 2/9, 1 1.222 . Note that all these relations are valid only for sufficiently high values of elastomer swelling ratio.
304
6.1 Modern views on kinetics of swelling of crosslinked elastomers in solvents
Figure 6.1.4. Kinetic (a) and strain (b) curves of elastomer swelling in toluene: 1 PBU-3; 2 PBU-4; 3 PBU-1; 4 PBU-2. [Adapted, by permission, from E. Ya. Denisyuk, V. V. Tereshatov, Vysokomol. soed., A42, 74 (2000)].
The obtained theoretical predictions have been verified in experiments on real elastomers. The elastomers tested in our experiments were amorphous polybutadiene urethanes (PBU) with polymer network of different density: 0.3 kmol/m3 (PBU-1), 0.05 kmol/m3 (PBU-2), 0.2 kmol/m3 (PBU-3), 0.1 kmol/m3 (PBU-4). Oligooxypropylene triol Laprol 373 was used as a crosslinking agent for curing of prepolymer of oligobutadiene diol. The elastomer specimens were manufactured in the form of disks, 35 mm in diameter, and 2 mm thick. The kinetics of specimen swelling was determined in low-molecular liquids: toluene, dibutyl sebacate (DBS), dioctyl sebacate (DOS). The typical kinetic and strain curves of free swelling are given in Figure 6.1.4.6 The S-shape of the kinetic swelling curves in terms of coordinates (t1/2, g1) is indicative of abnormal sorption. The values of parameters q and r were obtained from kinetic and strain curves using the regression method. The values of correlation coefficient were 0.997 0.999 and 0.994 0.998 respectively. The obtained data and Eqs. [6.1.45], [6.1.46] were then used to calculate s and d. The diffusion coefficients were defined by the kinetic curves in terms of Eq. [6.1.47] under the assumption that d = 2/9. The obtained results were summarized in Table 6.1.1.6 The analysis of these data shows that swelling of the examined elastomers is of power-mode type. The concentration dependence of the liquid diffusion coefficient defined by the parameter s is found to be rather weak. For elastomers under consideration no exponential or blow-up swelling modes have been observed. Table 6.1.1. Experimental characteristics of elastomer swelling kinetics6
q
r
s
d
D0, cm2/s
PBU-1/toluene
0.278
0.68
0.84
0
0.19
1.4×10-6
PBU-2/toluene
0.093
0.83
1.09
0.8
0.24
4.9×10-7
PBU-3/toluene
0.230
0.78
1.02
0.5
0.24
1.3×10-6
PBU-4/toluene
0.179
0.71
0.97
0
0.27
1.4×10-6
PBU-1/DBS
0.345
0.67
0.92
0
0.27
6.2×10-8
Elastomer/Liquid
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305
Table 6.1.1. Experimental characteristics of elastomer swelling kinetics6
q
r
s
d
D0, cm2/s
PBU-2/DBS
0.128
0.78
1.04
0.5
0.25
2.5×10-8
PBU-3/DBS
0.316
0.67
0.83
0
0.19
6.6×10-8
PBU-4/DBS
0.267
0.69
0.88
0
0.21
7.4×10-8
PBU-1/DOS
0.461
0.67
0.81
0
0.17
1.8×10-8
PBU-4/DOS
0.318
0.63
0.81
0
0.22
3.4×10-8
Elastomer/Liquid
It is of interest to note that experimental values of the parameter d characterizing the strain dependence of equilibrium swelling ratio for elastomers subjected to uniform biaxial extension closely approximate the theoretical values. It will be recalled that this parameter is specified by Eq. [6.1.21]. Moreover, the Flory theory defines it as d = 2/9 = 0.22(2), whereas the des Cloizeaux law provides d 0.205 , which suggests that the proposed model of elastomer swelling performs fairly well. 6.1.5 CONCLUSIONS In this section, we have developed a geometrically and physically nonlinear model of swelling processes for an infinite plane elastomeric layer and obtained approximate solutions describing different stages of swelling at large deformations of a polymeric matrix. We have identified the strain-stress state of the material caused by diffusion processes and analyzed its influence on the swelling kinetics. It has been found that a non-stationary boundary regime initiated by deformations arising in elastomer during swelling and increasing a thermodynamical compatibility of elastomer with a liquid is the main reason for swelling anomalies observed in the experiments. Anomalies of sorption kinetics turn out to be a typical phenomenon observable to one or another extent in elastic swelling materials. The theory predicts the possibility for qualitatively different diffusion modes of free swelling. A particular mode is specified by a complex of mechanical, thermodynamical, and diffusion material properties. The results of analytical and numerical solutions for a plane elastomer layer show that the swelling process may be governed by three different laws resulting in the power, exponential, and blow-up swelling modes. Experimentally it has been determined that in the examined elastomers the swelling mode is governed by the power law. The existence of exponential and blow-up swelling modes in real materials is still an open question. New methods have been proposed, which allow one to estimate the concentration dependence of liquid diffusion in elastomer and strain dependence of equilibrium swelling ratio under conditions of symmetric biaxial elastomer extension in terms of kinetic and strain curves of swelling. REFERENCES 1 2 3 4
A E Green, P M Naghdi, Int. J. Eng. Sci., 3, 231 (1965). A E Green, T R Steel, Int. J. Eng. Sci., 4, 483 (1966). K R Rajagopal, A S Wineman, MV Gandhi, Int. J. Eng. Sci., 24, 1453 (1986). M V Gandhi, K R Rajagopal, AS Wineman, Int. J. Eng. Sci., 25, 1441 (1987).
306 5 6 7 8 9 10
6.1 Modern views on kinetics of swelling of crosslinked elastomers in solvents E Ya Denisyuk, V V Tereshatov, Appl. Mech. Tech. Phys., 38, 913 (1997). E Ya Denisyuk, V V Tereshatov, Vysokomol. soed., A42, 74 (2000) (in Russian). P J Flory, Principles of polymer chemistry, Cornell Univ. Press, New York, 1953. V A Vasilyev, Yu M Romanovskiy, V G Yahno, Autowave Processes, Nauka, Moscow, 1987 (in Russian). P G De Gennes, Scaling Concepts in Polymer Physics, Cornell Univ. Press, Ithaca, 1980. A A Samarskiy, V A Galaktionov, S P Kurdyumov, A P Mikhaylov, Blow-up Modes in Problems for Quasilinear Parabolic Equations, Nauka, Moscow, 1987 (in Russian)
Vasiliy V. Tereshatov, Valery Yu. Senichev, and E. Ya Denisyuk
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6.2 EQUILIBRIUM SWELLING IN BINARY SOLVENTS Vasiliy V. Tereshatov, Valery Yu. Senichev, and E. Ya Denisyuk Institute of Continuous Media Mechanics and Institute of Technical Chemistry, Ural Branch of Russian Academy of Sciences, Perm, Russia Depending on the purposes and operating conditions of polymer material processing, the differing demands regarding solubility of low-molecular-mass liquids in polymers exist. Polymeric products designed for use in contact with solvents should be stable against adsorption of these liquids. On the contrary, the well dissolving polymer solvents are necessary to produce polymer films. The indispensable condition of creation of the plasticized polymer systems (for example, rubbers) is the high thermodynamic compatibility of plasticizers with the polymer matrix. Hence, it immediately follows the statement of the problem of regulation of thermodynamic compatibility of polymers with low-molecular-mass liquids in a wide range of its concentration in polymer material. The problem of compatibility of crosslinked elastomers with mixed plasticizers and volatile solvents is thus of special interest. Depending on ratios between solubility parameters of solvent 1, 1, solvent 2, 2, and polymer, 3, solvents can be distinguished as “symmetric” liquids and “non-symmetric” ones. The non-symmetric liquids are defined as a mixture of two solvents of variable composition, solubility parameters 1 and 2 which are larger or smaller than solubility parameter of polymer (2 > 1 > 3, 3 > 2 > 1). The symmetric liquid (SL) with relation to polymer is the mixture of two solvents, whose solubility parameter, 1, is smaller, and parameter, 2, is larger than the solubility parameter of polymer, 3. The dependence of equilibrium swelling on the non-symmetric liquid composition does not have a maximum, as a rule.1 Research on swelling of crosslinked elastomers in SL is of particular interest in the regulation of thermodynamic compatibility of network polymers and binary liquids. Swelling in such liquids is characterized by the presence of maximum on the curve of dependence of network polymer equilibrium swelling and composition of a liquid phase.2,3 The extreme swelling of crosslinked polymers of different polarity in SL was discussed elsewhere.3 The following elastomers were used as samples: a crosslinked elastomer of ethylene-propylene rubber SCEPT-40 [3 = 16 (MJ/m3)1/2, (ve/ V0)x = 0.24 kmol/m3], crosslinked polyester urethane, PEU, from copolymer of propylene oxide and trimethylol propane [3 = 18.3 (MJ/m3)1/2, (ve/V0)x = 0.27 kmol/m3], crosslinked polybutadiene urethane, PBU, from oligobutadiene diol [3 = 17.8 (MJ/m3)1/2, (ve/ V0)x = 0.07 kmol/m3] and crosslinked elastomer of butadiene-nitrile rubber [3 = 19 (MJ/ m3)1/2, (ve/V0)x = 0.05 kmol/m3]. The samples of crosslinked elastomers were swollen to equilibrium at 25oC in 11 SLs containing solvents of different polarity. The following regularities were established. With decrease in the solubility parameter value of component 1 (see Table 6.2.1) in SL (1 < 3), the maximum value of equilibrium swelling, Q, shifts to the field of larger concentration of component 2 in the mixture (Figures 6.2.1 and 6.2.2). On the contrary, with decrease in the solubility parameter 2 (see Table 6.2.1) of components 2 (2 > 3), the
308
6.2 Equilibrium swelling in binary solvents
Figure 6.2.1. Dependence of equilibrium swelling of PEU on the acetone concentration in the mixtures: 1 toluene-acetone, 2 cyclohexane-acetone, 3 heptane-acetone. [Adapted, by permission, from V. V. Tereshatov, M. I. Balashova, A. I. Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch of AS USSR Press, Sverdlovsk, 1989, p. 3.]
Figure 6.2.2. Dependence of equilibrium swelling of PBU on the DBP (component 2) concentration in the mixtures: 1 DOS-DBP, 2 TO-DBP, 3 decaneDBP. [Adapted, by permission, from V. V. Tereshatov, M. I. Balashova, A. I. Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch of AS USSR Press, Sverdlovsk, 1989, p. 3.]
maximum Q corresponds to composition of the liquid phase enriched by component 1 (Figure 6.2.3). Table 6.2.1. Characteristics of solvents and plasticizers at 298K. [Adapted, by permission, from V. V. Tereshatov, M. I. Balashova, A. I. Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch of AS USSR Press, Sverdlovsk, 1989, p. 3.] , kg/m3
V×106, m3
, (MJ/m3)1/2
Cyclohexane
779
109
16.8
Heptane
684
147
15.2
Solvent/plasticizer
Decane
730
194
15.8
Toluene
862
106
18.2
1,4-Dioxane
1034
86
20.5
Acetone
791
74
20.5
Ethyl acetate
901
98
18.6
Amyl acetate
938
148
17.3
Dibutyl phthalate
1045
266
19.0
Vasiliy V. Tereshatov, Valery Yu. Senichev, and E. Ya Denisyuk
309
Table 6.2.1. Characteristics of solvents and plasticizers at 298K. [Adapted, by permission, from V. V. Tereshatov, M. I. Balashova, A. I. Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch of AS USSR Press, Sverdlovsk, 1989, p. 3.] , kg/m3
V×106, m3
, (MJ/m3)1/2
Dioctyl sebacate
913
467
17.3
Transformer oil
890
296
16.0
Solvent/plasticizer
Figure 6.2.3. Dependence of equilibrium swelling of the crosslinked elastomer SCEPT-40 on the concentration of component 2 in the mixtures: 1 heptane-toluene, 2 heptane-amyl acetate, 3 heptane-ethyl acetate. [Adapted, by permission, from V. V. Tereshatov, M. I. Balashova, A. I. Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch of AS USSR Press, Sverdlovsk, 1989, p. 3.]
Figure 6.2.4. Dependence of equilibrium swelling of the crosslinked elastomer SCN-26 on the concentration of component 2 in the mixtures: 1 toluene-acetone, 2 ethyl acetate-dioxane, 3 ethyl acetateacetone. [Adapted, by permission, from V. V. Tereshatov, M. I. Balashova, A. I. Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch of AS USSR Press, Sverdlovsk, 1989, p. 3.]
Neglecting the change of volume on mixing, the solubility parameter of the mixture of two liquids is represented by: 12 = 1 1 + 2 2 where:
1 and 2 volume fractions of components 1 and 2
More exact evaluation of the 12 value is possible if the experimental data on enthalpy of mixing, H, of components of SL are taken into account:4
310
6.2 Equilibrium swelling in binary solvents 2
2
12 = 1 1 + 2 2 – H V 12
12
With a change in 1 and 2 parameters, the SL composition has the maximum equilibrium swelling which corresponds to shifts in the field of composition of the liquid phase. The 12 parameter is close or equal to the value of the solubility parameter of polymer. Such a simplified approach to the extreme swelling of polymers in liquid mixtures frequently works very well in practice. If there is a maximum on the curve of swelling in SL, then the swelling has an extreme character (11 cases out of 12) (Figures 6.2.1-6.2.4). The parameter of interaction, 123, between polymer and a two-component liquid can be used as a co-solvency criterion for linear polymers (or criterion of extreme swelling), more general, than the equality (12 = 3):5 123 = 13 1 + 23 2 – 1 2 12 where:
13 and 23 12
[6.2.1]
parameters of interaction of components 1 and 2 with polymer, correspondingly parameter of interaction of components 1and 2 of liquid mixture
In the equation obtained from the fundamental work by Scott,5 mixed solvent is represented as “a uniform liquid” with the variable thermodynamic parameters depending on composition. If the 123 value is considered as a criterion of existence of a maximum of equilibrium swelling of polymer in the mixed solvent, a maximum of Q should corresponds to the minimum of 123. For practical use of Eq. [6.2.2] it is necessary to know parameters 13, 23, and 12. The values 13 and 23 can be determined from the Flory-Rehner equation, using data on swelling of a crosslinked elastomer in individual solvents 1 and 2. The evaluation of the 12 value can be carried out with use of results of the experimental evaluation of vapor pressure, viscosity and other characteristics of a binary mixture.6,7 To raise the forecasting efficiency of prediction force of such criterion as 123 minimum, the amount of performance parameters determined experimentally must be reduced. For this purpose, the following expression for the quality criterion of the mixed solvent (the analogy with expression of the Flory-Huggins parameter for individual solvent-polymer system) is used: V 12 s 2 123 = 123 + ------- – 12 V 12 = V 1 x 1 + V 2 x 2 RT 3
[6.2.2]
where: V12 V1, V2 x1, x2 R T s 123
molar volume of the liquid mixture molar volumes of components 1 and 2 molar fractions of components 1 and 2 in the solvent universal gas constant temperature, K. constant, equal to 0.34 s
s
The values of entropy components of parameters 13 and 23 (essential for quality prediction)8 were taken into account. Using the real values of entropy components of s s interaction parameters 13 and 23 , we have:
Vasiliy V. Tereshatov, Valery Yu. Senichev, and E. Ya Denisyuk
311
V s 2 13 = 13 – -------1- 3 – 1 RT
[6.2.3]
V s 2 23 = 23 – -------2- 3 – 2 RT
[6.2.4]
quality criterion of solvent mixture is represented by:3 V 12 2 s s 123 = 13 1 + 23 2 + ------- 3 – 12 RT
[6.2.5]
The values of parameters 13 and 23 were calculated from the Flory-Rehner equas tion, using data on swelling of crosslinked polymer in individual solvents, the values 13 , s 23 , and 123 were estimated from Eqs. [6.2.3-6.2.5). Then equilibrium swelling of elastomer in SL was calculated from the equation similar to Flory-Rehner equation, considering the mixture as a uniform liquid with parameters 123 and V12 variable in composition. The calculated ratios of components of mixtures, at which the extreme swelling of elastomers is expected, are given in Table 6.2.2. Table 6.2.2. Position of a maximum on the swelling curve of crosslinked elastomers in binary mixtures. [Adapted, by permission, from V. V. Tereshatov, M. I. Balashova, A. I. Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch of AS USSR Press, Sverdlovsk, 1989, p. 3.] Elastomer PEU
PBU
SCN-26
Binary mixture
Components ratio, wt% Calculation
Experiment
toluene-acetone
90/10
90/10
cyclohexanone-acetone
40/60
50/50
heptane-acetone
30/70
25/25
decane-DBP
30/70
30/70
TO-DBP
40/60
40/60
DOS-DBP
60/40
50/50
ethyl acetate-acetone
70/30
70/30
ethyl acetate-acetone
70/30
70/30
ethyl acetate-1,4-dioxane
Results of calculation of the liquid phase composition at maximum swelling of elastomer correlate with the experimental data (see Table 6.2.2). The approach predicts the existence of an extremum on the swelling curve. This increases the forecasting efficiency of the prediction. The application of “approximation of the uniform liquid” (AUL) for prediction of extreme swelling of crosslinked elastomers is proven under condition of coincidence of composition of a two-component solvent in a liquid phase and in the swollen elastomer.
312
6.2 Equilibrium swelling in binary solvents
Results of study of total and selective sorption by crosslinked elastomers of components of SLs are given below.3 Crosslinked PBU [(ve/V0) = 0.20 kmol/m3] and crosslinked elastomer of butadienenitrile rubber SCN-26 [(ve/V0) = 0.07 kmol/m3] were used in this study. The tests were carried out at 25±0.10oC in the following mixtures: n-nonane-tributyl phosphate (TBP), nhexane-dibutyl phthalate (DBP), n-hexane-dibutyl maleate (DBM), and dioctyl sebacate (DOS)-diethyl phthalate (DEP). A crosslinked elastomer SCN-26 was immersed to equilibrate in amyl acetate-dimethyl phthalate mixture. Liquid phase composition was in range of 5 to 10%. A sol-fraction of samples (plates of 0.9×10-2 m diameter and in 0.3×10-2 m thickness) was preliminary extracted with toluene. For high accuracy of the analysis of binary solvent composition, a volatile solvent, hexane, was used as a component of SL in most experiments. Following the attainment of equilibrium swelling, the samples were taken out of SL and held in air until the full evaporation of hexane, that was controlled by constant mass of sample. A content of a nonvolatile component of SL in elastomer was determined by the difference between the amount of liquid in the swollen sample and the amount of hexane evaporated. In the case of SL with nonvolatile components (such as, DBP or DOS) the ratio of SL components in the swollen PBU was determined by the gas-liquid chromatography, for which purpose toluene extract was used. The volume fractions of components 1 and 2 of SL in a liquid phase 1 and 2 were calculated on the basis of their molar ratio and densities 1 and 2. Volume fraction of polymer, 3 , in the swollen sample was calculated from the equation: 1 3 = --------------Qv + 1 where: QV
volume equilibrium swelling of elastomer in SL.
Volume fractions 1 and 2 of components 1 and 2 of low-molecular-mass liquids inside the swollen gel were determined from the equation: i i = ------------- , (i = 1,2) 1 – 3 where:
i
volume fraction of i-component related to the total volume of its low-molecular-mass part (not to the total volume of three-component system)
The results of study of sorption of two-component liquids in PBU and in crosslinked elastomer SCN-26 are shown in Figures 6.2.5-6.2.8, as dependencies of Qv on the volume fraction 2 of component 2 in a liquid phase and on the volume fraction 2 of component 2 of SL that is a part of the swollen gel. The data vividly show that extremum swelling of crosslinked elastomers in SL can be observed in all investigated cases. At the maximum value of Qv, the compositions of SL in the liquid phase and in the swollen elastomer practically coincide ( 2 2 ).
Vasiliy V. Tereshatov, Valery Yu. Senichev, and E. Ya Denisyuk
Figure 6.2.5. Dependence of equilibrium swelling of PBU on the 2 value for DEP in the liquid phase (1) and the 2 value inside the gel (1') swollen in the mixture DOS-DEP.
313
Figure 6.2.6. Dependence of equilibrium swelling of PBU on the 2 value for DEP in the liquid phase (curves 1 and 2) and the 2 value inside the swollen gel (curves 1' and 2') in the mixtures: 1,1'-hexane(1)DBM(2), 2,2'- hexane(1)-DBP(2).
The total sorption can be determined by the total content of the mixed solvent in the swollen skin9 or in the swollen elastic network (these results). The dependencies of Qv on 2 (Figures 6.2.5-6.2.8) reveal the influence of liquid phase composition on the total sorption. The total sorption of the binary solvent by polymer can also be measured by the value of the volume fraction of polymer in the swollen gel9 because the value of 3 is unequally related to the volume fraction of the absorbed liquid, 3 = 1 – 1 + 2 . At the fixed total sorption (Qv or 3 = const) the preferential sorption, e, an be found from the following equation: Figure 6.2.7. Dependence of equilibrium swelling of PBU on the 2 value for TBP in the liquid phase (1) and the 2 value in the gel (1') swollen in the mixture: nonane-TBP.
= 1 – 1 = 2 – 2
314
6.2 Equilibrium swelling in binary solvents
Figure 6.2.8. Dependence of equilibrium swelling of crosslinked elastomer SCN-26 on the 2 value for DMP in the liquid phase (1) and the 2 value in the gel (1'), swollen in the mixture: amyl acetate-DMP.
Figure 6.2.9. Experimental dependence of the preferential sorption on the volume fraction 2 of component 2 in the liquid phase: 1 DOS(1)-DEP(2)PBU(3), 2 hexane(1)-DBP(2)-PBU(3), 3 hexane(1)-DBM(2)-PBU(3), 4 amyl acetate(1)DMP(2)-SCN-26(3), 5 nonane(1)-TBP(2)-PBU(3).
At the same values of Qv difference between coordinates on the abscissa axes of points of the curves 1-1' , 2-2' (Figures 6.2.5-6.2.8) are equal (Figure 6.2.9). As expected,10 preferential sorption was observed, with the essential distinction of molar volumes V1 and V2 of components of the mixed solvent (hexane-DBP, DOS-DEP). For swelling of the crosslinked elastomer SCN-26 in the mixture of components, having similar molar volumes V1 and V2 (e.g., amyl acetate-dimethyl phthalate) the preferential sorption of components of SL is practically absent. Influence of V1 and V2 and the influence of double interaction parameters on the sorption of binary liquids by crosslinked elastomers was examined by the method of mathematical experiment. Therewith the set of equations describing swelling of crosslinked elastomers in binary mixture, similar to the equations obtained by Bristow6 from the Flory-Rehner theory11 and from the work of Schulz and Flory,12 were used: 2
2
2
ln 1 + 1 – I 2 + 12 2 = ln 1 + 1 – I 2 + 3 + 12 2 + 12 3 + + 12 + 13 – I 23 2 3 + e V 3 V 1 3
13
–1
–1
2
2 – --- 3 f
[6.2.6]
–1
ln 2 + 1 – I 1 + 1 12 1 = ln 2 + 1 – I 1 + 3 + –1
2
2
13
+ I 12 1 + I 23 3 + 12 + I 23 – 13 1 3 + e V 3 V 2 3
2 – --- 3 f
[6.2.7]
Vasiliy V. Tereshatov, Valery Yu. Senichev, and E. Ya Denisyuk
315
where: l f
= V1/V2 functionality of a network
The analysis of calculations from Eqs. [6.2.6] and [6.2.7] has shown that if V1 < V2, the preferential sorption is promoted by difference in parameters of interaction, when 12 > 13. The greater is 12 value at V 1 V 2 the more likely preferential sorption takes place with all other parameters being equal. The same applies to the diluted polymer solutions. To improve calculations of the preferential sorption in the diluted solutions of polymers, the correction of Flory's theory is given in works9,13-15 by introduction of the parameter of three-component interaction, T, into the expression for free energy of Figure 6.2.10. Experimental data and calculated depenmixing, and substitution of T by qT.14 This dence of equilibrium fraction of components 1 (1), 2 (2), and 3 (3) in PBU sample swollen in the hexane- approach is an essential advancement in the DBP mixture on the 2 value for DBP in the liquid analysis of a sorption of two-component phase: lines calculation, points experimental. liquids by polymer. On the other hand, the increase in the number of experimental parameters complicates the task of prediction of the preferential sorption. In swelling crosslinked elastomers, the preferential sorption corresponds to the maximum Qv value and compositions in a swollen polymer and a liquid phase practically coincide (Figures 6.2.5-6.2.8). This observation can be successfully used for an approximate evaluation of the preferential sorption. Assuming that and at extremum of the total sorption (min), AUL5 e can be used to calculate the effective value of 12 from the expression for 16 m
13 23 V 1 123 V 1 e - + ------------- – --------------------- 12 = -----m m m m m 2 1 V 2 V 12 1 2
[6.2.8]
where: m e 12
the index for the maximum of sorption. the value, calculated from the equation [6.2.8], substitutes 12 from the Eqs. [6.2.6] and [6.2.7]
The results of calculations are presented as dependencies of volume fractions, 2, and 3 of the triple system components (swollen polymer) vs. the volume fraction 2 (or 1) of the corresponding components of the liquid phase (Figures 6.2.10 and 6.2.11). For practical purposes it is convenient to represent the preferential sorption as the dependence of equilibrium composition of a binary liquid (a part of the swollen gel) vs. composition of the liquid phase. These calculated dependencies (solid lines) and experimental (points)
316
6.2 Equilibrium swelling in binary solvents
Figure 6.2.11. Dependence of equilibrium fraction of components 1 (1), 2 (2), and 3 (3) in SCN-26 sample swollen in the amyl acetate-DMP mixture on the 2 value for DMP in the liquid phase: lines calculation, points experimental.
Figure 6.2.12. Dependence of equilibrium 2 value on the 2 value in the liquid phase: 1 amyl acetate(1)DMP(2)-SCN-26(3), 2 hexane(1)-DBM(2)-PBU(3), 3 nonane(1)-TBP(2)- PBU (3); lines calculation, points experimental.
data for three systems are given in Figure 6.2.12. The results of calculations based on AUL, are in the satisfactory agreement with experimental data. Hence the experimentally determined equality of concentrations of SL components in the swollen gel and in the liquid phase allows one to predict composition of liquid, whereby polymer swelling is at its maximum, and the preferential sorption of components of SL. To refine dependencies of 1 on 1 or 2 on 2, correction can be used, for example, minimization of the square-law deviation of calculated and experimental data on the total sorption of SL by polymer. Thus it is necessary to account for proximity of the compositions of solvent in the swollen gel and the liquid phase. REFERENCES 1 2 3 4 5 6 7 8 9 10 11
A Horta, Makromol. Chem., 182, 1705 (1981). V V Tereshatov, V Yu Senichev, A I Gemuev, Vysokomol. Soedin., 32B, 422 (1990). V V Tereshatov, M I Balashova, A I Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch. of AS USSR Press, Sverdlovsk, 1989, p. 3. A A Askadsky, Yu I Matveev, Chemical structure and physical properties of polymers, Chemistry, Moscow, 1983. R L Scott, J. Chem. Phys., 17, 268 (1949). C M Bristow, Trans. Faraday Soc., 55, 1246 (1959). A Dondos, D Patterson, J. Polym. Sci., A-2, 5, 230 (1967). L N Mizerovsky, L N Vasnyatskaya, G M Smurova, Vysokomol. Soedin., 29A, 1512 (1987). J Pouchly, A Zivny, J. Polym. Sci., 10, 1481 (1972). W R Krigbaum, D K Carpenter, J. Polym. Sci., 14, 241 (1954). P J Flory, J Rehner, J. Chem. Phys., 11, 521 (1943).
Vasiliy V. Tereshatov, Valery Yu. Senichev, and E. Ya Denisyuk 12 13 14 15 16
A R Shulz, P J Flory, J. Polym. Sci., 15, 231 (1955). J Pouchly, A Zivny, J. Polym. Sci., 23, 245 (1968). J Pouchly, A Zivny, Makromol. Chem., 183, 3019 (1982). R M Msegosa, M R Comez-Anton, A Horta, Makromol. Chem., 187, 163 (1986). J Scanlan, J. Appl. Polym. Sci., 9, 241 (1965).
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6.3 SWELLING DATA ON CROSSLINKED POLYMERS IN SOLVENTS Vasiliy V. Tereshatov and Valery Yu. Senichev Institute of Technical Chemistry Ural Branch of Russian Academy of Sciences, Perm, Russia Data on equilibrium swelling of selected crosslinked elastomers in different solvents are presented in Table 6.3.2. All data were obtained in the author's laboratory during 5 years of experimental work. The network density values for these elastomers are given in Table 6.3.1. The data can be used for the quantitative evaluation of thermodynamic compatibility of solvents with elastomers and for calculation of Z, the thermodynamic interaction parameter. These data can be recalculated to the network density distinguished by the network density value, given in Table 6.3.1, using Eq. [4.2.9]. Network density values can be used for calculation of the interaction parameter. It should be noted that each rubber has specific ratio for the equilibrium swelling values in various solvents. This can help to identify rubber in polymeric material. Temperature influences swelling (see Subchapter 4.2). Equilibrium swelling data at four different temperatures are given in Table 6.3.3. Polymer samples were made from industrial rubbers. The following polyols were used for preparation of polyurethanes: butadiene diol (M~2000) for PBU, polyoxybutylene glycol (M~1000) for SCU-PFL, polyoxypropylene triol (M~5000) for Laprol 5003, polydiethylene glycol adipate (M~2000) for P-9A and polydiethylene glycol adipate (M~800) for PDA. Polyurethanes from these polyols were synthesized by reaction with 2,4-toluylene diisocyanate with addition of crosslinking agent trimetylol propane, PDUE, synthesized by reaction of oligobutadiene isoprene diol (M~4500) with double excess of 2,4-toluylene diisocyanate, followed by the reaction with glycidol. Table 6.3.1. Network density values for tested elastomers (data obtained from the elasticity modulus of samples swollen in good solvents) Elastomer
Trade mark
Network density, (kmol/m3)×102
Silicone rubber
SCT (1)
6.0
Butyl rubber
BR (2)
8.9
Polybutadiene rubber
SCDL (3)
40.5
Ethylene-propylene rubber
SCEPT (4)
2.7
Isoprene rubber
SCI-NL (5)
8.9
Butadiene-nitrile rubber
SCN-26 (6)
5.1
Polydiene-urethane-epoxide
PDUE (7)
16.0
Polybutadiene urethane
PBU (8)
20.8
Polyoxybutylene glycol urethane
PFU (9)
10.0
320
6.3 Swelling data on crosslinked polymers in solvents
Table 6.3.1. Network density values for tested elastomers (data obtained from the elasticity modulus of samples swollen in good solvents) Elastomer Polyoxypropylene glycol urethane
Trade mark
Network density, (kmol/m3)×102
Laprol 5003 (10)
43.0
Polydiethylene glycol adipate urethane P-9A (11)
6.4
Polydiethylene glycol adipate urethane PDA (12)
9.6
Table 6.3.2 Equilibrium swelling data (wt%) at 25oC. Elastomer number identifies elastomer (see the second column in Table 6.3.1) Solvent\elastomer*
1
2
3
4
5
6
7
8
9
10
11
122
78
16
44
4
137
84
16
42
0
101
32
0
7
139
28
1
155
315
39
24
238
3
53
4
12
Hydrocarbons Pentane
355
75
Hexane
380
305
Heptane
367
357
Isooctane
380
341
Decane
391
Cyclohexane
677
Transformer oil
47
214
105
586
30
881
10
1020 230
1580
600
3 0.5
Toluene
384
1294
435
492
356
134
315
77
31
Benzene
233
511
506
479
359
158
340
175
73
0-Xylene
515
496
356
122
288
53
42
87
2
22
2
41
0.1
Ethers Diamyl
310
Diisoamyl
333
220
889
584
791 120
Diethyl of diethylene glycol
85
1,4-Dioxane
248 33
Didecyl Dioctyl
20
428
180
896
156
702
7
168
11
203
6
242
3
251
23
1 54
264
178
782
48
192
848
133
213
88
317
251
121
64
40
210
238
48
35
249
36
Tetrahydrofuran
Esters of monoacids Heptyl propionate
260
236
Ethyl acetate
20
Butyl acetate
55
304
382
287
55
562
170
Isobutyl acetate
48
267
Amyl acetate
82
343
Isoamyl acetate
74
Heptyl acetate
213
236
100
545
100
Methyl capronate
369
285
115
Isobutyl isobutyrate
328
276
64
22 6 260
36
26
6
6
Vasiliy V. Tereshatov and Valery Yu. Senichev
321
Table 6.3.2 Equilibrium swelling data (wt%) at 25oC. Elastomer number identifies elastomer (see the second column in Table 6.3.1) Solvent\elastomer*
1
2
3
4
5
6
7
8
9
10
11
12
Esters of multifunctional acids Dihexyl oxalate
28
350
73
166
11
9
Diethyl phthalate
6
837
47
93
165
272
496
126
Dibutyl phthalate
9
767
123
154
121
228
47
20
187
9
Dihexyl phthalate
570
Diheptyl phthalate Dioctyl phthalate
37 8
28
189
Dinonyl phthalate
211
181
Didecyl phthalate
1
33
1.4
23
Diamyl maleate
425
Dimethyl adipate
560
Diamyl adipate Dihexyl adipate
197
71
0.5 232
19
14
246
716
6
294
203
88
295
199
42
2
2
126
12
0.6
280
Dioctyl adipate Dipropyl sebacate
8
20
Diamyl sebacate
70
Diheptyl sebacate Dioctyl sebacate
3
29
60 13
160
127
2 118
445
39
Triacetin
34
Tricresyl phosphate
800
Tributyl phosphate
261
162
5.5
15
28
45 300
74
3 0.4
0.7
489
129
256
93
105
327
523
140 244
238
80
Ketones Cyclohexanone Acetone
577 7
44
88
218
99
72
7
12
Alcohols Ethanol
49
Butanol
25
16
Pentanol
28
33
66
10
5
Hexanol
46
34
62
9
4
67
19
Heptanol
36
Nonanol
57
3
Halogen compounds CCl4
2830
284
999
584
Chlorobenzene
234
Chloroform
1565
Fluorobenzene
66 277
114
572
616
205
113
Nitrogen compounds Diethyl aniline
336
Dimethylformamide
52
120
34 918
322
6.3 Swelling data on crosslinked polymers in solvents
Table 6.3.2 Equilibrium swelling data (wt%) at 25oC. Elastomer number identifies elastomer (see the second column in Table 6.3.1) Solvent\elastomer*
1
2
3
4
5
6
7
8
9
10
11
12
277
298
242
377
799
241
Capronitrile
769
142
Acetonitrile
47
69
Nitrobenzene
Aniline
115
84
16
323 317
423
*See Table 6.3.1 for elastomer’s name
Table 6.3.3 Equilibrium swelling data (wt%) at -35, -10, 25, and 50oC Solvent\Elasto mer
Laprol*
SCU-PFL
P-9A
PBU
SCN-26
Isopropanol
8,12,37,305
8,19,72
8,10,18,28
3,5,18,28
20,23,26,41
Pentanol
27,34,80,119
16,25,78,104
7,9,10,18
8,9,33,52
31,37,49,60
Acetone
80,366,381,-
80,122,132,-
48,73,218,-
56,321,347,-
162,254,269,382
Ethyl acetate
214,230,288,314
113,114,133,138
209,210,210,213
165,171,187,257
324,343,395,407
Butyl acetate
294,304,309,469
119,122,123,125
41,44,64,80
288,293,307,473
404,426,518,536
Isobutyl acetate
259,259,288,-
89,92,100,105
23,28,48,57
210,212,223,348
309,326,357,362
Amyl acetate
315,309,315,426
124,136,144,155
16,18,36,44
285,297,298,364
343,347,358,359
Tetrahydrofuran
91,96,97,119
119,177,192,-
838,840,848,859
45,51,57,80
145,150,166,-
o-Xylene
363,368,389,471
117,121,122,137
24,25,53,60
328,357,369,375
428,440,405,406
Chlorobenzene
522,537,562,-
241,242,242,246
238,244,277,333
517,528,559,698
967,973,985,1256
Acetonitrile
19,21,28,33
23,26,39,41
254,263,323,362
6,10,16,27
47,47,47,82
Hexane
50,52,61,75
2,3,9,14
4,4,4,28
51,56,63,80
Toluene
360,366,380, 397
120,122,134,149
50,57,77,85
331,339,372,415
*(ve/V) = 0.149 kmol/m3. Network density values for other elastomers correspond to Table 6.3.2
Vasiliy V. Tereshatov and Valery Yu. Senichev
323
6.4 INFLUENCE OF STRUCTURE ON EQUILIBRIUM SWELLING Vasiliy V. Tereshatov and Valery Yu. Senichev Institute of Technical Chemistry Ural Branch of Russian Academy of Sciences, Perm, Russia Swelling of single-phase elastomers is, with other parameters being equal, limited by the chemical network. Microphase separation of hard and soft blocks can essentially influence swelling of block-copolymers. Hard domains formed in this process are knots of physical network, which can be resistant to action of solvents.1-4 Swelling of polyurethane blockcopolymers with urethane-urea hard segments is investigated. The maximum values of swelling, Qmax, of segmented polyurethane (prepolymer of oligopropylene diol with functional isocyanate groups) cured with 4,4’-methylene-bis-o-chloroaniline (MOCA) are given in Tables 6.4.1 and 6.4.2. The prepolymer Vibratane B 600 was obtained by the reaction of oligopropylene diol with 2,4-toluylene diisocyanate. The swelling experiments were carried out in four groups of solvents of different polarity and chemical structure.5 The effective molecular mass of elastically active chains, Mc, between network crosslinks was estimated from the Flory-Rehner equation.6 The interaction parameter of solvent with polymer was determined by calculation. In the first variant of calculation, a classical method based on the solubility parameter concept, was used with application of Bristow and Watson's semi-empirical relationship for 1:7 V 2 s 1 = 1 + -------1- 1 – p RT where:
s
1 V1 R1 T 1 and p
[6.4.1]
a lattice constant whose value can be taken as 0.34 the molar volume of the solvent the gas constant the absolute temperature the solubility parameters of the solvent and the polymer, respectively
However, to evaluate 1 from Eq. [6.4.1], we need accurate data for 1. In some cases the negative Mc values are obtained (Tables 6.4.1). The reason is that the real values of the entropy component of the 1 parameter can strongly differ from the 0.34 value. Table 6.4.1. Characteristics of polyurethane-solvent systems at 25oC. [Adapted, by permission, from U.S. Aithal, T.M. Aminabhavi, R.H. Balundgi, and S.S. Shukla, JMS - Rev. Macromol. Chem. Phys., 30C (1), 43 (1990).] Penetrant
Qmax
1
Mc
0.378
630
Monocyclic aromatics Benzene
0.71
324
6.4 Influence of structure on equilibrium swelling
Table 6.4.1. Characteristics of polyurethane-solvent systems at 25oC. [Adapted, by permission, from U.S. Aithal, T.M. Aminabhavi, R.H. Balundgi, and S.S. Shukla, JMS - Rev. Macromol. Chem. Phys., 30C (1), 43 (1990).] Penetrant
Qmax
1
Mc
Toluene
0.602
0.454
790
p-Xylene
0.497
0.510
815
Mesitylene
0.402
0.531
704
Chlorobenzene
1.055
0.347
905
Bromobenzene
1.475
0.347
1248
o-Dichlorobenzene
1.314
0.357
1106
Anisole
0.803
0.367
821
Nitrobenzene
1.063
0.356
835
Methanol
0.249
1.925
-90
Aliphatic alcohols Ethanol
0.334
0.349
172
n-Propanol
0.380
0.421
484
Isopropanol
0.238
0.352
249
n-Butanol
0.473
2.702
-131
2-Butanol
0.33
1.652
-307
2-Methyl-1-propanol
0.389
0.440
535
Isoamyl alcohol
0.414
0.357
398
Halogenated aliphatics Chloroform
4.206
0.362
3839
Bromoform
5.583
0.435
4694
1,2-Dibromoethane
1.855
0.412
770
1,3-Dibromopropane
1.552
0.444
870
Dichloromethane
2.104
0.34
1179
Trichloroethylene
1.696
0.364
1098
Tetrachlorethylene
0.832
0.368
429
1,2-Dichlorethane
1.273
0.345
728
Carbon tetrachloride
1.058
0.538
860
1,4-Dichlorobutane
0.775
0.348
626
1,1,2,2-Tetrachloroethane
5.214
0.34
6179
Miscellaneous liquids Methyl acetate
0.494
0.341
370
Ethyl acetate
0.509
0.422
513
Ethyl benzoate
0.907
0.34
1111
Vasiliy V. Tereshatov and Valery Yu. Senichev
325
Table 6.4.1. Characteristics of polyurethane-solvent systems at 25oC. [Adapted, by permission, from U.S. Aithal, T.M. Aminabhavi, R.H. Balundgi, and S.S. Shukla, JMS - Rev. Macromol. Chem. Phys., 30C (1), 43 (1990).] Qmax
1
Mc
Methyl ethyl ketone
1.261
0.364
2088
Tetrahydrofuran
2.915
0.39
2890
Penetrant
1,4-Dioxane
2.267
0.376
2966
DMF
1.687
1.093
-1184
DMSO
0.890
1.034
-975
Acetonitrile
0.184
0.772
182
Nitromethane
0.302
1.160
5737
Nitroethane
0.463
0.578
382
n-Hexane
0.069
1.62
2192
Cyclohexane
0.176
0.753
287
Benzyl alcohol
4.221
In the second variant of evaluation of Mc, data on the temperature dependence of volume fraction of polymer, 2, in the swollen gel were used. Results of calculations of Mc from the Flory-Rehner equation in some cases also gave negative values. The evaluation of Mc in the framework of this approach is not an independent way, and Mc is an adjustment parameter, as is the parameter 1 of interaction between solvent and polymer. Previous evaluation of the physical network density of SPU was done on samples swollen to equilibrium in two solvents.2,9,10 Swelling of SPU in toluene practically does not affect hard domains.9,11 Swelling of SPU (based on oligoether diol) in a tributyl phosphate (a strong acceptor of protons) results in full destruction of the physical network with hard domains.2 The effective network density was evaluated for samples swollen to equilibrium in toluene according to the Cluff-Gladding method.12 Samples were swollen to equilibrium in TBP and the density of the physical network was determined from equation:2,10 v e V 0 dx – v e V 0 x = v e V 0 d
[6.4.2]
As the result of unequal influence of solvents on the physical network of SPU, the values of effective density of networks calculated for the “dry” cut sample can essentially differ. The examples of such influence of solvents are given in the work.2 SPU samples with oligodiene soft segments and various concentration of urethane-urea hard blocks were swollen to equilibrium in toluene, methyl ethyl ketone (MEK), tetrahydrofuran (THF), 1,4-dioxane and TBP (experiments 1-6, 9, 10, 12). SPU based on oligoether (experiment 7), with urethane-urea hard segments, and crosslinked single-phase polyurethanes (PU) on the base of oligodiene prepolymer with functional isocyanate groups, cured by oligoether triols (experiments 8, 11) were also used. The effective network densities of materials swollen in these solvents were evaluated by the Cluff-Gladding method
326
6.4 Influence of structure on equilibrium swelling
through the elasticity equilibrium modulus. The data are given in Table 6.4.2 per unit of initial volume. Table 6.4.2. Results of the evaluation of equilibrium swelling and network parameters of PUE. [Adapted, by permission, from E.N. Tereshatova, V.V. Tereshatov, V.P. Begishev, and M.A. Makarova, Vysokomol. Soed., 34B, 22 (1992).] #
kg/m3
Qv
ve/V0
Toluene
Qv
ve/V0 THF
Qv
ve/V0
MEK
Qv
ve/V0
Qv
1,4-Dioxane
ve/V0 TBP
1
996
1.56
1.03
0.46
0.77
1.08
0.41
3.76
0.12
5.12
0.06
2
986
2.09
0.53
0.52
0.43
1.40
0.23
6.22
0.04
11.15
0.02
0.73
0.01
3
999
1.74
0.77
0.49
4
1001
2.41
0.44
0.49
5
1003
4.46
0.15
0.47
6
984
2.63
0.40
0.57
1.11
0.38
7.88
0.03
18.48
1.75
0.13
14.3
0.02
0.19
3.44
0.14
4.21
3.29
0.39
1.45 1.40
0.73
1.86
0.31
7.22
0.04
1.01
0.54
2.08
0.34
1.48
0.35
7
1140
0.86
1.83
2.06
8
972
2.42
0.35
1.84
0.36
9
979
2.26
0.39
1.72
0.37
10
990
2.00
0.63
0.47
0.08
0.98
0.54
1.97
0.35
1.62
0.31
0.99
0.55
2.42
0.29
2.19
0.24
11
991
4.11
0.18
2.79
0.18
3.98
0.17
3.42
0.18
2.54
0.17
12
997
2.42
0.50
1.00
0.32
2.68
0.12
4.06
0.13
4.32
0.08
(ve/V0), kmol/m3
The data shows that the lowest values of the network density are obtained for samples swollen to equilibrium in TBP. Only TBP completely breaks down domains of hard blocks. If solvents, which are acceptors of protons (MEK, THF, 1,4-dioxane), are used in swelling experiment an intermediate values are obtained between those for toluene and TBP. The network densities of SPU (experiments 8 and 11) obtained for samples swollen in toluene, TBP, 1,4-dioxane and THF coincide (Table 6.4.2).2 To understand the restrictions to swelling of SPU caused by the physical network containing hard domains, the following experiments were carried out. Segmented polybutadiene urethane urea (PBUU) on the base of oligobutadiene diol urethane prepolymer with functional NCO-groups (M 2400 ), cured with MOCA, and SPU-10 based on prepolymer cured with the mixture of MOCA and oligopropylene triol (M 5000 ) were used. The chemical network densities of PBUU and SPU were 0.05 and 0.08 kmol/m3, respectively. The physical network density of initial sample, (ve/V0)d, of PBUU was 0.99 kmol/m3 and of SPU-10 was 0.43 kmol/m3. Samples of PBUU and SPU-10 were swollen to equilibrium in solvents of different polarity: dioctyl sebacate (DOS), dioctyl adipate (DOA), dihexyl phthalate (DHP), trans-
Vasiliy V. Tereshatov and Valery Yu. Senichev
327
former oil (TM), nitrile of oleic acid (NOA), dibutyl carbitol formal (DBCF), and tributyl phosphate (TBP). The values of equilibrium swelling of elastomers in these solvents, Q1, (ratio of the solvent mass to the mass of the unswollen sample) are given in Table 6.4.3. After swelling in a given solvent, samples were swollen in toluene to equilibrium. The obtained data for T swelling in toluene, Q V , indicate that the physical networks of PBUU and SPU-10 do not change on swelling in most solvents. Equilibrium swelling in toluene of initial sample and the sample previously swollen in other solvents is practically identical. Several other observations were made from swelling experiments, including sequential application of different solvents. If preliminary disruption of the physical network of PBUU and SPU-10 by TBP occurs, swelling of these materials in toluene strongly increases. Similarly, samples previously swollen in TBP have higher equilibrium swelling, Q2, when swollen in other solvents. The value of Q2 is likely higher than equilibrium swelling Q1 of initial sample (Table 6.4.3). Q2 for PBUU is closer to the value of equilibrium swelling of a single-phase crosslinked polybutadiene urethane, PBU, having chemical network density, (ve/V0)x = 0.04 kmol/m3. Thus, the dense physical network of polyurethane essentially limits the extent of equilibrium swelling in solvents, which does not breakdown the domain structure of a material. Table 6.4.3. Equilibrium swelling of SPBUU and SPU-10 (the initial sample and sample after breakdown of hard domains by TBP) and swelling of amorphous PBU at 25oC SPBUU Solvent
Initial structure Q1
-
QT
SPU-10
After breakdown of domains
Initial structure
Q2
Q1
1.35
After breakdown of domains
PBU
Q2
Q3 5.56
QT 2.10
DOS
0.62
1.34
3.97
0.66
2.09
3.04
DOA
0.68
1.34
4.18
0.84
2.05
3.26
DBP
0.60
1.36
3.24
0.90
2.12
3.38
DHP
0.63
1.34
3.71
0.85
2.10
3.22
4.47
TO
0.57
1.35
2.29
0.58
2.07
1.92
1.99
NOA
0.59
1.36
4.03
0.72
2.10
2.86
4.66
DBCP
0.69
1.37
4.60
0.155
2.96
3.45
5.08
TBP
5.01
7.92*
5.01
4.22
5.43
4.22
* The result refers to the elastomer, having physical network completely disrupted
Swelling of SPU can be influenced by changes in elastomer structure resulting from mechanical action. At higher tensile strains of SPU, a successive breakdown of hard domains as well as micro-segregation may come into play causing reorganization.13-15 If
328
6.4 Influence of structure on equilibrium swelling
the structural changes in segmented elastomers are accompanied by breakdown of hard domains and a concomitant transformation of a certain amount of hard segments into a soft polymeric matrix or pulling of some soft blocks (structural defects) out of the hard domains,14 variation of network parameters, is inevitable. It is known4 that high strains applied to SPU causes disruption of the physical network and a significant drop in its density. Table 6.4.4. Equilibrium swelling of SPU-1 samples in various solvents before and after stretching at 25oC (calculated and experimental data). [Adapted, by permission, from V.V. Tereshatov, Vysokomol. soed., 37A, 1529 (1995).] Solvent
1 kg/m3
V1×103 m3/kmol
Qv (=0)
1 (=0)
Qv (=700%) calc
exp
T
QV
(=700%)
T
QV
(=0)
Toluene
862
107
3.54
0.32
5.06
4.87
DBP
1043
266
1.12
0.56
1.47
1.53
4.85
3.49
n-Octane
698
164
0.79
0.75
0.90
0.93
4.94
3.60
Cyclohexane
774
109
1.46
0.60
1.78
1.95
4.99
3.63
p-Xylene
858
124
2.94
0.36
4.17
3.93
4.81
3.52
Butyl acetate
876
133
2.28
0.44
3.13
2.97
5.12
3.69
DOS
912
468
1.21
0.38
1.60
1.71
5.10
3.63
DOA
924
402
1.49
0.32
2.19
2.18
5.00
3.61
DHS
923
340
1.74
0.30
2.55
2.44
5.01
3.59
DHP
1001
334
1.25
0.47
1.71
1.74
4.79
3.47
DBCP
976
347
4.48
4.51
9.92
9.98
The data on equilibrium swelling of SPU-1 with oligodiene soft segments obtained by curing prepolymer by the mixture of MOCA and oligobutadiene diol (M 2000 ) with the molar ratio 1/1 are given in Table 6.4.4. The initial density of the SPU-1 network v e V 0 dx = 0.206 kmol/m3, the physical network density v e V 0 d = 0.170 kmol/ m3. After stretching by 700% and subsequent unloading, the value v e V 0 dx = 0.115 kmol/m3 and v e V 0 d = 0.079 kmol/m3. The density of the chemical network v e V 0 x = 0.036 kmol/m3 did not change. Samples were swollen to equilibrium in a set of solvents: toluene, n-octane, cyclohexane, p-xylene, butyl acetate, DBCF, DBP, DHP, dihexyl sebacate (DHS), DOA and DOS (the values of density, 1, and molar volume of solvents, V1, are given in Table 6.2.5). The data in Table 6.4.4 shows that, after stretching, the volume equilibrium swelling of samples does not change in DBCF.4 In other solvents equilibrium swelling is noticeably increased. Swelling experiments of samples previously swollen in solvents and subsequently in toluene have shown that the value of equilibrium swelling in toluene varies only for samples previously swollen in DBCF. The effective network densities evaluated for SPU-1 samples, swollen in DBCF, and then in toluene, have appeared equal (0.036 and 0.037
Vasiliy V. Tereshatov and Valery Yu. Senichev
329
kmol/m3, respectively) and these values correspond to the value of the chemical network parameter, (ve/V0)x, of SPU-1. It means that DBCF breaks down the physical network of elastomer; thus, the values of Qv in DBCF do not depend on the tensile strain. In all other cases, swelling of SPU-1 in toluene differs only marginally from the initial swelling of respective samples in toluene alone. Therefore, these solvents are unable to cause the breakdown of the physical network. The calculation of equilibrium swelling of SPU-1 (after its deformation up to 700% and subsequent unloading) in a given solvent was carried out using the Flory-Rehner equation. In our calculations we used values of the 1 parameter of interaction between solvents and elastomer calculated from experimental data of equilibrium swelling of initial sample ( = 0) in these solvents. The difference between calculated and experimental data on equilibrium swelling of SPU-1 samples after their deformation does not exceed 9%. Therefore, the increase in swelling of SPU-1 is not related to the change in the 1 parameter but it is related to a decrease in the (ve/V0)dx value of its three-dimensional network, caused by restructure of material by effect of strain. The change of the domain structure of SPU exposed to increased temperature (~200oC) and consequent storage of an elastomer at room temperature may also cause a change in equilibrium swelling of material.16 REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
V.P. Begishev, V.V. Tereshatov, E.N. Tereshatova, Int. Conf. Polymers in extreme environments, Nottingham, July 9-10, 1991, Univ. Press, Nottingham, 1991, pp. 1-6. E.N. Tereshatova, V.V. Tereshatov, V.P. Begishev, and M.A. Makarova, Vysokomol. Soed., 34B, 22 (1992). V.V. Tereshatov, E.N. Tereshatova, V.P. Begishev, V.I. Karmanov, and I.V. Baranets, Polym. Sci., 36A, 1680 (1994). V.V. Tereshatov, Vysokomol. soed., 37A, 1529 (1995). U.S. Aithal, T.M. Aminabhavi, R.H. Balundgi, and S.S. Shukla, JMS-Rev. Macromol. Chem. Phys., 30C (1), 43 (1990). P.J. Flory, Principles of Polymer Chemistry, Cornell Univ. Press, Ithaca, 1953. G.M. Bristow, and W.F. Watson, Trans. Faraday. Soc., 54, 1731 (1958). L.N. Mizerovsky, L.N. Vasnyatskaya, and G.M. Smurova, Vysokomol. Soed., 29A, 1512 (1987). D. Cohen, A. Siegman, and M. Narcis, Polym. Eng. Sci., 27, 286 (1987). E. Konton, G. Spathis, M. Niaounakis and V. Kefals, Colloid Polym. Sci., 26B, 636 (1990). V.V. Tereshatov, E.N. Tereshatova, and E.R. Volkova, Polym. Sci., 37A, 1157 (1995). E.E. Cluff, E.K. Gladding, and R. Pariser, J. Polym. Sci., 45, 341 (1960). Yu.Yu. Kercha, Z.V. Onishchenko, I.S. Kutyanina, and L.A. Shelkovnikova, Structural and Chemical Modification of Elastomers, Naukova Dumka, Kiev, 1989. Yu.Yu. Kercha, Physical Chemistry of Polyurethanes, Naukova Dumka, Kiev, 1979. V.N. Vatulev, S.V. Laptii, and Yu.Yu. Kercha, Infrared Spectra and Structure of Polyurethanes, Naukova Dumka, Kiev, 1987. S.V. Tereshatov, Yu.S. Klachkin, and E.N. Tereshatova, Plastmassy, 7, 43 (1998).
Vasiliy V. Tereshatov, Vladimir N. Strelnikov, and Marina A. Makarova
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6.5 EFFECT OF STRAIN ON THE SWELLING OF NANO-STRUCTURED ELASTOMERS Vasiliy V. Tereshatov, Vladimir N. Strelnikov, and Marina A. Makarova Institute of Technical Chemistry, Ural Branch of Russia Academy of Sciences, Perm, Russia Nano-heterogeneous elastomers with alternating soft and hard segments are used widely as compared with other block-copolymers having H-bonds. These are, for example segmented polyurethane ureas, SPUU, segmented polyurethanes, SPU, elastomers on the base of oligodiene urethane epoxides and so on.1-3 A significant difference in polarity leads to the microphase segregation of hard and soft segments with formation of hard segments' domains. These domains with sizes of 5-50 nm play a role of reinforcing fillers and crosslinking points of specific physical networks stable at elevated temperatures.1,4 Various combinations of physical-chemical and physical-mechanical properties of segmented elastomers, SE, can be achieved by changing the chemical structure of oligomers having terminated functional groups, diisocyanates, and low-molecular-mass chain extenders. It was determined that a dense physical network having crosslinking points forming hard domains is characteristic of segmented polyurethane ureas. This physical network limits swelling of SPUU in organic liquids that cannot dissolve hard domains. Exploitation of elastic products made from SE can be associated with appearing of great local deformations for example during periodical loading. Structure of these polymers can change at high deformations; domains of hard blocks are partially destroyed with formation of smaller domains; primary orientation takes place not only for soft segments, but for hard segments as well. Some hard segments are drawn out from some domains.5-9 As a result the density of physical network having crosslinking points forming hard domains can change. Sorption properties of a material in contact with low-molecular liquids can also change. This subchapter is devoted to the effect of strain on the sorption of organic solvents (plasticizers) by SE with various chemical and supramolecular structure. The sorption of liquids was compared before strain and after strain up to fixed values. The change in molecular and supramolecular structure of SPUU samples with soft segments of different polarity was investigated by the FTIR-spectroscopy method. It was made for the clarification of reasons of the effect of preliminary strain on the sorption of low-molecular-mass liquids, and for analysis of obtained results. Polyether urethane urea SPUU-T with polytetramethylene oxide soft segments (average molecular mass of soft segments M n =1430 g mol-1), polybutadiene urethane urea SPUU-D(M n = 2100 g mol-1), and polyurethane urea SPUU-TD with mixed polybutadiene and polytetramethylene oxide soft segments were investigated. The quantity of polar and non-polar soft segments was uniform for SPUU-TD. Materials were manufactured using a two stage technology. The first stage was reaction of 2,4-toluenediisocyanate and oligodiols: oligobutadienediol OBD (M n = 2100 g mol-1) and oligotetramethylene oxide diol OTM (M n = 1430 g mol-1). The ratio NCO/OH
332
6.5 Effect of strain on the swelling of nano-structured elastomers
was 2.03 at this stage. Prepolymers were cured at the second stage by methylene-bisortho-chloroaniline, MOCA, at 90oC for 3 days. The completeness of conversion of NCOgroups was controlled by the FTIR-spectroscopy. The methods of samples manufacturing are given elsewhere.10 Also, single-phase polyurethane PUE-TL was synthesized for comparison of sorption properties of this material and nano-heterogeneous SPUU. PUE-TL was synthesized on the base of prepolymer of OTM cured by mixture of the initial OTM and oligopropylene oxide triol Laprol 373 (M n = 370 g mol-1). FTIR-spectra of samples' surfaces were registered by the multiple attenuated total reflectance (MATR) method using the IFA-66/S spectrometer and specially designed MATR accessories with 45o KRS-5 trapezoid as the internal reflection element (operating number of reflections 1000). Tests were conducted using samples cut according to crystal size 20 40 mm2, thickness 2 mm before and after stretching up to the given strain value. The 20 80 mm2 sheets were stretched, then samples for spectra registration were cut off from working parts of sheets. The density of samples was determined by the hydrostatic method using AR-240 balance (Ohaus, Switzerland) with accuracy 2x10-7 kg. The density of physical network, which crosslinking points are hard domains, and the density of chemical network with chemical crosslinking points, was determined for SPUU using an approach developed by the authors.11 The total network density Ndx was determined using the compression modulus of samples swollen in toluene. Swelling in this solvent doesn't affect hard domains. The chemical network density Nx was determined testing samples swollen in tributyl phosphate. The physical network density was determined using difference Ndx Nx = Nd. For single-phase polyurethane Ndx = Nx (Nd = 0). Low-molecular-mass liquids, such as di-2(ethylhexyl) phthalate, DEHP, and liquid chlorinated paraffin HP-470 (M n =470 g mol-1) were used to investigate the strain effect on the sorption properties of SE and single-phase elastomer with a similar structure. Parts of samples were preliminary drawn up to 350%. Cylindrical specimens (5 mm diameter, 2 mm thickness) cut from drawn samples were immersed in the above mentioned liquids up to achievement of the constant mass at the temperature 25±1oC. Parts of non-drawn samples were immersed in these liquids up to equilibrium as well. The equilibrium swelling Q, wt%, and equilibrium concentration Cp, wt%, at swelling were determined. Q = 100m1/m0 where: m1 m0
mass of absorbed liquid initial mass of sample
Cp = 100m1/(m1 + m0) Table 6.5.1 contains data values for Q, Cp for three heterogeneous elastomers with urethane urea hard segments and a single-phase polyurethane PUE-TL. It is seen that preliminary strain = 350% does not practically affect the equilibrium swelling and the equilibrium concentration of this material at swelling in DEHP and HP-470.
Vasiliy V. Tereshatov, Vladimir N. Strelnikov, and Marina A. Makarova
333
Table 6.5.1. Swelling data for SPUU and PUE-TL samples in DEHP and HP-470. DEHP Sample
= 0%
HP-470 = 350%
= 0%
= 350%
Q, wt% Cp, wt% Q, wt% Cp, wt% Q, wt% Cp, wt% Q, wt% Cp, wt% SPUU-D
62.6
38.5
70.1
41.2
47.5
32.2
53.8
35.0
SPUU-TD
40.6
28.9
53.8
35.0
44.3
30.7
58.7
37.0
SPUU-T
28.4
22.1
40.8
29.0
40.6
28.9
61.2
38.0
PUE-TL
187
65.2
186
65.0
154
60.6
156
60.9
Figure 6.5.1. FTIR-MATR spectra of SPUU-D (a), SPUU-T (b), and SPUU-TD(c).
The effect of strain differs significantly for swelling of SE with non-polar soft segments (SPUU-D) and ones with polar polyether segments (SPUU-T). Intermediate position in swelling value belongs to SPUU-TD with mixed soft segments. Preliminary strain affects equilibrium swelling of SPUU-D only a little. The values Q, and Cp for SPUU-T change significantly after strain.
334
6.5 Effect of strain on the swelling of nano-structured elastomers
The reason for this effect can be found out from the qualitative analysis of FTIR MATR spectra for SPUU-D, SPUU-TD, SPUU-T before and after strain up to 350%. (Figure 6.5.1). It is seen that integral spectral curve changes little after strain of SPUU-D with non-polar soft segments (Figure 6.5.1a). The band intensity of carbonyl at 1640 cm-1 decreases only a little after strain. This band refers to the absorption of hydrogen-bonded, ordered urea carbonyl. Urea groups are usually linked mutually (self-associates of urea groups) and localized in domains of the hard segments. The intensity of this band can be used for comparison of the microphase segregation degree for soft and hard segments.6 It is suggested that the band at 1663 cm-1 (1663-1666 cm-1) refers to the absorption of hydrogen-bonded, disordered urea carbonyls in the soft phase of polymer. The intensity of this band also changes little after the strain of SPUU-D (Figure 6.5.1a). Significant changes in the SPUU-T spectrum are seen after strain up to 350% (Figure 6.5.1b). The intensity of the band at 1642 cm-1 decreases significantly (the band of carbonyl absorption shifts by 2 cm-1 to the side of higher values of the wave number), that shows decreasing in the degree of microphase segregation of hard and soft segments. The concentration of hard phase in a material decreases as well. The intensity of band at 1729 cm-1 for free urethane carbonyl and band at 1711 cm-1 for hydrogen-bonded, disordered urea carbonyl in the soft phase of polymer increases. Thus, redistribution of intensity of carbonyl absorbance in hard and soft phase of polyurethane urea is seen. The assignment of carbonyl bands is based on results published elsewhere.12-15 The degree of microphase segregation of hard and soft segments in SPUU-TD decreases less than in SPUU-T, but more than in SPUU-D (Figure 6.5.1c). The results of the analysis of FTIR MATR spectra and data for change in physical network density (for network with hard domains playing a role of crosslinking points) after strain of investigated materials correlate (Table 6.5.2). The value Nd for physical network decreases from 1.42 to 1.1 kmol/m3 for SPUU-T, from 1.09 to 0.88 kmol/m3 for SPUU-TD, from 0.78 to 0.68 kmol/m3 for SPUU-D. The data permit to explain differences in sorption values for SPUU after strain. Table 6.5.2. Network parameters for SPUU and single-phase polyurethane PUE-TL before strain and after strain up to 350% N, kmol/m3 Material
, kg/m3
Ndx
Nx
Mdx, kg/kmol
Nd
0
350%
0
350%
0
350%
0
350%
SPUU-T
1100
1.42
1.10
0.04
0.04
1.38
1.06
770
1000
SPUU-TD
1041
1.09
0.88
0.04
0.04
1.05
0.84
955
1180
SPUU-D
989
0.78
0.68
0.05
0.05
0.73
0.63
1270
1450
PUE-TL
1056
0.14
0.14
0.14
0.14
0
0
7600
7600
The decrease in the Nd value (for physical network) and data on the spectral analysis show the partial rupture of hard domains. A part of hard segments transfers to the soft
Vasiliy V. Tereshatov, Vladimir N. Strelnikov, and Marina A. Makarova
335
phase after straining. As a result the volume of polymer available for plasticizer molecules increases. Therefore, two factors promote the increase of solubility of SPUU in liquids: decrease in the physical network density and the increase in the volume fraction of soft phase in heterogeneous polymer.These factors affect swelling of SPUU-TD with polyether soft segments to higher degree after straining. The equilibrium swelling Q and concentration of liquid in SPUU change after strain less in the case when some soft polyether segments are replaced by polydiene segments. Lower rupture of hard domains leads to the little change in swelling values for polydieneurethane urea in DEHP and HP-470. An effect of strain on swelling of segmented polyurethane SPU and three polyurethane ureas SPUU-TD, SPUU-1, and SPUU-P was investigated for 11 polar and non-polar solvents (plasticizers). Molecular mass of polytetramethylene oxide soft segments and polypropylene oxide soft segments (Mn) is 1000 g mol-1 in SPUU-1. Polyurethane was synthesized via curing of prepolymer OTM (M n = 2000 g mol-1) by BD. Synthesis of prepolymer was conducted using diphenylmethane diisocyanate, MDI. The molar ratio NCO/ OH = 0.98. The molar ratio OTM/MDI = 2.2. The methods of sample manufacture are given elsewhere.10 The values of an effective network density Nd for SPU, SPUU-TD, SPUU-1, and SPUU-P are 0.56, 1.05, 1.75, 1.30 kmol/m3, respectively. Samples were swollen at 25±1oC before the strain and after strain up to the value 350% in the following liquids: ethyl acetate, n-octane, p-xylene, toluene, butyl acetate, isoamyl alcohol, DEHP, dibutyl phthalate, DBP, dibutyl sebacate, DBS, di-(2-ethylhexyl) sebacate, DEHS, and tributyl phosphate, TBP. The results show that samples of linear SE are completely solvable in TBP which is a strong acceptor of protons independent of the structure and polarity of soft segments. The physical network with crosslinking points which are hard domains limits equilibrium swelling in many solvents. This is clearly seen from an example of SPUU-1 with high effective density of such network Ndx = 1.75 kmol/m3. The Q value in the majority of solvents is below 50% (Table 6.5.3). The maximal sorption was obtained for segmented polyurethane with lower physical network density. Preliminary strain leads to increase in plasticizer sorption. Thus, determined peculiarities are characteristic for segmented heterogeneous elastomers with urethane urea and urethane hard segments. It is interesting to note that strain affects the swelling of SE in many liquids with the less degree in the case of low network density Nd value. This is evidently seen for example of SPU. Table 6.5.3. Equilibrium swelling of segmented polyurethane and polyurethane ureas in solvents (plasticizers). Solvent (plasticizer)
Q, % ( = 0)
Q, % ( = 350)
SPUU-TD
SPUU-1
SPU
SPUU-P
SPUU-TD
SPUU-1
SPU
SPUU-P
Ethyl acetate
64
45
120
116
78
60
133
132
Octane
22
6
15
7
28
7
19
8
p-Xylene
89
48
128
14
6
146
336
6.5 Effect of strain on the swelling of nano-structured elastomers
Table 6.5.3. Equilibrium swelling of segmented polyurethane and polyurethane ureas in solvents (plasticizers). Solvent (plasticizer)
Q, % ( = 0)
Q, % ( = 350)
SPUU-TD
SPUU-1
SPU
SPUU-P
SPUU-TD
SPUU-1
SPU
SPUU-P
Toluene
106
57
158
74
130
78
174
86
Butyl acetate
71
44
135
94
89
62
142
109
Isoamyl alcohol
24
29
70
28
38
73
DEHP
41
15
72
7
54
24
77
10
BBP
48
35
41
63
53
58
DBS
48
26
95
38
65
40
99
48
DEHS
29
10
41
39
14
43
TBP
872
878
CONCLUSIONS The effect of preliminary strain on the sorption of liquids of various chemical structure by segmented polyurethane and polyurethane ureas was investigated. It was shown that the swelling degree increases after strain as a result of partial destruction of domain structure and decrease in effective density of the physical network formed by hard domains. It was determined that increase in destruction of domain structure of a material leads to further change in solubility of liquids in an elastomer. This effect is less pronounced in low dense networks and disappears at all in the case of absence of such network (for single-phase elastomers). However in this last case effect of limiting swelling in various liquids due the presence of physical network stable to the solvent action decreases, or disappears. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Z.S. Petrovic, J.Ferguson, J. Polym. Sci., 16, 695 (1991). D. Randall, S. Lee, The polyurethanes book. Wiley, New York, 2003. T. Thomson, Polyurethanes as specialty chemicals: principles and applications, CRC Press, Boca Raton, 2005. V. V.Tereshatov, V. N.Strel'nikov, M. A. Makarova, V. Yu. Senichev, and E. R.Volkova, Russ. J. Appl. Chem., 83, 1380 (2010). F. Yeh, B.S. Hsiao, B.B. Sauer, S. Michel, H.W. Siesler, Macromolecules, 36, 1940 (2003). E.M. Christenson, J.M. Anderson, A. Hiltner, E. Baer, Polymer, 46, 1744 (2005). G. Muller-Riederer, R. Bonart, Progr. Colloid. Polym. Sci., 62, 99 (1977). R. Bonart, K. Hoffman, Colloid Polym. Sci., 260, 268 (1982). V.V. Tereshatov, Polym. Sci., 37, 946 (1995). V.V. Tereshatov, M.A. Makarova, V.Yu. Senichev, A.I. Slobodinyuk, Colloid Polym. Sci., 290, 641 (2012). V.V. Tereshatov, E.N. Tereshatova, E.R.Volkova, Polym. Sci., 37, 1157 (1995). R.W. Seymor, G.M. Estes, S.L. Cooper, Macromolecules, 3, 579 (1970). L. Ning, W. De-Nung, Y. Sheng-Kang, Macromolecules, 30, 4405 (1997). V.V. Tereshatov, M.A. Makarova, E.N. Tereshatova, Polym. Sci. A., 46, 1332 (2004). C.M. Brunette, S.L. Hsu, W.J. MacKnight, Macromolecules, 15, 71 (1982).
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6.6 THE EFFECT OF THERMODYNAMIC PARAMETERS OF POLYMERSOLVENT SYSTEM ON THE SWELLING KINETICS OF CROSSLINKED ELASTOMERS Vasiliy V. Tereshatov, Elena R. Volkova, Evgeniy Ya. Denisyuk, and Vladimir N. Strelnikov Institute of Technical Chemistry Ural Branch of Russian Academy of Sciences, Perm, Russia Swelling of polymeric materials is a special case of mechanic-diffusion processes, i.e. cooccurring and interrelated processes of the fluid diffusion and strain of a material. Threedimensional non-linear theory1 of such processes was used to study swelling of elastomeric polymer networks in low-molecular solvents elsewhere.2,3 A mathematical model describing the non-equilibrium swelling process flowing at finite strains was developed for a flat elastomer sample or a polymer gel.2 Regularities of non-equilibrium processes of polymer networks swelling were described at very low swelling degrees4-6 and at high swelling degrees.2-4 However, the actual swelling process is accompanied usually by a finite strain of a material, the amount of which is determined by the quality of a solvent and varies widely. This subchapter presents the results of theoretical and experimental studies on the influence of solvent properties on the nature of the swelling kinetics for elastomeric polymer networks at finite strains of the polymer matrix. Emphasis is focused on the study of the relationship of the asymptotic properties of the swelling kinetic curves with the thermodynamic quality of a solvent. The chemical potential of a solvent in the sample under swelling is given by the following equation:2 2
–1 4 3 –1 –4
= RT ln 1 – + + + Z E where:
V1, V2 Z = V2/V1 E =
[6.6.1]
Flory-Huggins parameter molar volumes of a solvent and the same for subchains of polymer network dimensionless parameter local volume fraction of a polymer in the swollen sample volume fraction of a polymer in the swollen material at equilibrium longitudinal elongation of the sample under swelling.
Equation [6.6.1] is written in the reference configuration. This configuration corresponds to the state of a material at equilibrium swelling. This means that = 1 in this state, 13 and = E for the initial (unswollen) state. For this reason, h is one half of the sample thickness in the equilibrium swollen state. The reference state is the state of the material, which is considered as unstrained; thereafter a strain is determined with respect to it. In the case of swellable materials any state of undistorted material, in which solvent is distributed uniformly over its volume, can be used as a reference configuration.1,2 Equation [6.6.1] describes the dependence of the chemical potential of a solvent absorbed by the sample under symmetrical biaxial stretching and compression. Equating it
338
6.6 The effect of thermodynamic parameters of polymer-solvent system
to zero, we obtain an equation that can be used to calculate the equilibrium swelling 13 degree of a sample under these conditions. In particular, if = E , we obtain the following equation 2
–1 –1
ln 1 – + + + Z
= 0
[6.6.2]
which determines the local swelling degree on the sample surface during the time of immersion in the solvent. When = 1, we obtain the well-known Flory-Rehner equation 2
–1 1 3
ln 1 – E + E + E + Z E
= 0
[6.6.3]
The kinetic curve is an integral characteristic of the swelling process g = u x
[6.6.4]
which is usually determined by swelling experiments.7 The diffusion kinetics of flat sample swelling depends on the parameters and Z. Flory-Huggins parameter is a quantitative measure of the thermodynamic quality of a solvent for the given polymer. For good solvents < 0.5, and for the bad ones > 0.5. The value of = 0.5 corresponds to the so-called -solvents. As is shown below, the value determines largely the swelling kinetics. The value of Z affects the equilibrium swelling degree of the material. Next, we consider the elastomeric polymer networks and low-molecular-weight solvents for which Z >> 1. The initial part of the kinetic curve is described by the following equation:8 g = M
q
[6.6.5]
Curves of distribution of diffusing liquid on the sample thickness are presented for various times (dimensionless) in the earlier reference.8 = tD/h2, where t swelling time (with dimension); D diffusion coefficient; h one half of the sample thickness. Figure 6.6.1 shows that dimensionless boundary concentration of solvent u1 differs significantly from 1 for a good solvent ( < 0.5) and for a -solvent ( = 0.5) as well. This means that the liquid concentration on the boundary of the sample-liquid contact at the initial swelling stage is significantly less than equilibrium value u = 1. In the case of a poor solvent u 1 1 . Swelling kinetic curves are described by the law of normal sorption ( > 0.5). When < 0.5 swelling curves are S-shaped ones. Kinetic curves of swelling of a sample in a good solvent shown in the coordinates ( ; g) are S shaped, and their initial region described by equation [6.6.1] with the parameter q > 0.5. Figures 6.6.1 and 6.6.2 show the results of numerical solution of the boundary problem for a variety of solutions of . One can see how the nature of the diffusion process and the shape of swelling kinetic curves changes depending on the deterioration of the thermodynamic quality of solvent. Particularly, it can be seen that as the parameter FloryHuggins increases the interval of the boundary concentration decreases, and swelling kinetic curves transform to kinetic curve of the normal sorption. The swelling kinetics of polydiene-urethane epoxide crosslinked elastomer (PDUE) was investigated for the experimental verification of the theoretical analysis. It was pro-
Vasiliy V. Tereshatov et al.
339
Figure 6.6.1. Distribution of the fluid during diffusion at different time points = tD/h2 for swelling of a plane layer in a good solvent ( = 0), in a -solvent ( = 0.5), and in a poor solvent ( = 0.8) 1) = 0.01; 2) = 0.1; 3) = 0.2; 4) = 0.4; 5) = 0.6; 6) = 0.8; 7) = 1.0; 8) = 1.5. The curves were obtained at Z = V2/V1 = 200. [Adapted, by permission, from E.Ya. Denisyuk, E.R. Volkova, Vysokomolek. Soed., 45A, 1160 (2003).]
vided for solvents with different thermodynamic quality: dioctyl sebacate (DOS), dioctyl adipate (DOA), dibutyl sebacate (DBS), dioctyl phthalate (DOP), CCl4, toluene, dibutylcarbitolformal (DBKF), dimethyl adipate (DMA), and triacetin.8 PDUE elastomer was obtained by curing oligodiene (vinyl-isoprene) urethane epoxide (M = 5×103) by oligodivinyl carboxylate-terminated oligomer SKD-KTR (M = 3×103) at the molar ratio of 1:0.56. Samples of elastomers were cured for 4 days at 80°C.
340
6.6 The effect of thermodynamic parameters of polymer-solvent system
Figure 6.6.2. Theoretical kinetic curves for swelling of a flat layer at different values of the Flory-Huggins parameter and fixed value of Z = V2/V1 = 200: 1) = 0; 2) = 0.4; 3) = 0.5; 4) = 0.6; 5) = 1.0. [Adapted, by permission, from E.Ya. Denisyuk, E.R. Volkova, Vysokomolek. Soed., 45A, 1160 (2003).]
Figure 6.6.3. The experimental kinetic curves of PDUE samples swelling in solvents of different thermodynamic quality: DOS ( = 0), DOA ( = 0.02), DBS ( = 0.132), DBKF ( = 0.46), and DMA ( = 0.93).
Molar volume of the polymer network chains V2 was evaluated by the shear modulus G of a sample swollen in toluene up to equilibrium. The parameter value was estimated for each solvent using equation [6.6.3]. Kinetic curves of swelling were calculated according to the formula g(t) = m(t)/mE, where m(t), mE current value of the mass of a liquid absorbed by sample and finite one, respectively. Experiments were carried out by swelling at 25oC. Figure 6.6.3 shows the kinetic curves of the samples PDUE swelling in solvents of different thermodynamic quality. Table 6.6.1 shows the experimental values of the parameters characterizing the swelling kinetics. Table 6.6.1. Parameters of kinetic curves of swelling of PDUE elastomer in solvents of various thermodynamic quality. [Adapted, by permission, from E.Ya. Denisyuk, E.R.
Volkova, Vysokomolek. Soed., 45A, 1160 (2003)]. E
Z
u, %
q
qexp
Dx1011, m2/s
DOS
0.157
0.0
35
64
0.68
0.665
0.81
DOA
0.156
0.02
41
64
0.7
0.665
2.25
DBS
0.161
0.132
49
63
0.7
0.660
3.29
DOP
0.181
0.152
41
61
0.71
0.652
0.71
CCl4
0.0917
0.218
170
69
0.67
0.674
32.8
DBKF
0.291
0.460
47
47
0.58
0.603
1.89
DMA
0.654
0.930
94
4.2
0.52
0.506
2.26
Triacetin
0.943
2.1
87
0.14
0.50
0.500
0.24
Solvent
Vasiliy V. Tereshatov et al.
341
It is seen from Figure 6.6.3 and Table 6.6.1 how the kinetic curves of elastomer swelling transform when the quality of the solvent decreases. For example, these curves are S-shaped ones for solvents with smaller than 0.5. This is evidenced by the fact that the parameter q > 0.5, and its value is close to the value of 0.7 corresponding to the limited self-similar regime of swelling of a material in good solvents at a constant diffusion coefficient. S-shape of the kinetic curve of swelling in DBKF is defined poorly, but its properties are close to -solvents. Kinetic curves of swelling in DMA, which is a poor solvent for a given polymer, have the shape characteristic for the kinetic curves of normal sorption. They have a distinct linear region, and the S-shape is absent. This corresponds to the value of q 0.5 . As previously shown,8 the determination of the diffusion coefficient D should be provided in analyzing the final section of the kinetic curve of swelling. This curve is described by the universal expression 2 –1
g t = 1 – C exp – 1 h Dt
[6.6.6]
where: g (t) t C h D 1
the ratio of the current mass value of an absorbed liquid to the equilibrium one time of swelling constant one half of the sample thickness in the reference configuration diffusion coefficient of a solvent in material. the first positive root of the equation n = tg n .
The value , taking into account the properties of a solvent, is determined using the following equation:8 4 1 – E = ---------------------------------------------------------------------------53 3 Z E 1 – 2 1 + 2 1 E + 1
[6.6.7]
In this case, the diffusion coefficient D includes physical parameters and geometric factors associated with the particular mode of the strain process of polymer matrix during swelling. In addition, it depends essentially on the choice of the reference state, which is necessary to fix the description of the swelling process. It was shown that such choice was ambiguous.2 Any undistorted state can be used as the reference state when material is not subjected to the mechanical stresses, and the fluid is uniformly distributed in volume. However, the situation is simpler in the case of materials with low swelling degree. Here geometric factors play a minor role and the size of the sample differs slightly in the “dry” state and in the swollen one. The diffusion coefficient D is weakly dependent on the choice of the reference state; it can be approximately regarded as a physical characteristic of the process. The efficiency of the theory is demonstrated for the single-phase crosslinked polyurethane elastomers. At low degrees of swelling of materials in liquids, equation [6.6.6] can be transformed with simplification into the expression:
342
6.6 The effect of thermodynamic parameters of polymer-solvent system 2
kh D = -------21
[6.6.8]
where: h 1 2 k
one half of the sample thickness in the equilibrium swollen state for poor solvents and materials with low swelling degree2 slope coefficient, calculated on the final sections of the kinetic curves of swelling, plotted in coordinates (t;ln(1 g)).
Expression [6.6.8] describes the kinetics of the normal absorption of liquid in the presence of which the spatial polymer network remains unchanged (absence of chemical network destruction). In the case of micro-heterogeneous materials with block structure, such as segmented polyurethanes and polyurethane ureas, the absorption of the liquid should not lead to the chemical network destruction, and to the destruction of the physical network having crosslinking points forming hard domains. This subchapter presents the results of a study on the absorption kinetics of a number of liquids for segmented polyether urethane urea. Estimation of the diffusion coefficient of liquids was made for crosslinked polymers with a spatial network where crosslinking points are caused by chemical bonds and hard segment domains. The object of the study was a micro-heterogeneous polyurethane urea (PUU) based 3 on the prepolymer SKU-PFL-100 (M 1.4 10 ), synthesized by the interaction of oli3 gotetramethylene oxide diol (M 1 10 ) with a double excess of 2,4-toluene diisocyanate. MOCA (aromatic diamine: 3,3’-dichloro-4,4’-diaminodiphenyl methane) was used to cure SKU-PFL-100. The NCO/NH2 ratio was 1.2 for this reaction. Prepolymer was degassed at 50 10 oC before the reaction. Reaction mixture was stirred for 3 minutes at 50 1 oC and a residual pressure of 1-2 kPa after injection of melted aromatic diamine. Curing period was 3 days at 80 2 oC. Cured samples were further stored at the room temperature for at least 30 days. Sorption kinetics of elastomer was studied for following liquids: toluene, DBS, DOA, and transformer oil (TO). The study of the kinetics of swelling was conducted using samples manufactured in the form of discs of 35 mm in diameter and 2 mm in thickness. The kinetics of swelling was measured gravimetrically. A sample was immersed in a plasticizer and periodically weighed using analytical balance. The experiment time was determined via establishment of the equilibrium concentration of a solvent in sample. Experiments were carried out at 24 1 °C. Determination of spatial network parameters for elastomers was determined before achievement of the value of the equilibrium swelling of the elastomer in the liquid and after it. Total effective network density Ndx of chemical network and physical network of a polymer resulting from its domain structure, and the density of chemical network Nx were determined by the method described elsewhere.9 Properties of used liquids and the network parameters are shown in Table 6.6.2. Estimation of the network parameters for polymer network shows that the values Ndx and Nx remain almost unchanged before swelling of the polymer in organic liquids and after it. This, according to the previous study,10
Vasiliy V. Tereshatov et al.
343
demonstrates the stability of not only chemical but also the physical network of the polymer to the action of the liquids. Based on the data on the total network density, Ndx, and equilibrium swelling of PUU according to the Flory-Rehner equation11 the estimation of the parameter (polymer-liquid interaction) was made for used liquids. Table 6.6.2. Properties of low-molecular-mass liquids and PUU samples swollen in them. [Adapted, by permission, from V.V. Tereshatov, E.R. Volkova, E.Ya. Denisyuk,
Plastmassy, 13, No.12, 14 (2004).] Solvent
Molar vol. V, cm3/mol
Eq. swelling Q, %
Network density, kmol/m3
1
kx102, s-1
Dx1012, m2/s
Ndx
Nx
1.67
0.22
TO
300
6.8
1.67
0.22
1.7
0.72
0.53
DOA
399
12.6
1.67
0.22
1.2
0.75
0.61
DBS
336
17.8
1.67
0.22
1.0
0.93
0.83
Toluene
106
46.8
1.67
0.22
0.7
47.1
43.0
Figure 6.6.4. Kinetic curves for swelling of PUU in toluene, DBS, DOA, and TO. [Adapted, by permission, from V.V. Tereshatov, E.R. Volkova, E.Ya. Denisyuk, Plastmassy, 13, No.12, 14 (2004).]
Figure 6.6.5. Dependences for calculation of k coefficient for the final stage of PUU swelling in toluene, DBS, DOA, and TO. [Adapted, by permission, from V.V. Tereshatov, E.R. Volkova, E.Ya. Denisyuk, Plastmassy, 13, No.12, 14 (2004).]
Figure 6.6.4 shows the results of a study of the kinetics of absorption of low-molecular-mass liquid by polymer. It can be seen that all swelling kinetic curves plotted in the coordinates ( t ; g), have an initial linear stage, i.e., kinetic curves are normal sorption ones. Consequently, the experimental values of the diffusion coefficient D, can be calculated using equation [6.6.8]. Figure 6.6.5 shows the swelling kinetic curves plotted in the coordinates (t;ln(1 g)). They take the shape of straight lines with a slope coefficient k at
344
6.6 The effect of thermodynamic parameters of polymer-solvent system
g 0.4 . Diffusion coefficients for PUU and non-volatile liquids DBS, DOA, TO, and volatile solvent toluene were determined using obtained k values (Table 6.6.2). The results of calculations show that the diffusion coefficients of DBS, DOA, and TO in PUU differ only a little. The diffusion coefficient of toluene is many times higher due to the fact that its molar volume V1 is much smaller. Increase in D during swelling of polymer in toluene according to the previous data8 is also a natural consequence of the greater thermodynamic affinity for toluene to PUU comparing with other solvents. This can be seen from the values of parameter 1 shown in Table 6.6.2. Results of investigations show that the proposed approach is quite justified to describe the kinetics of swelling of segmented polyurethanes in low-molecular-mass liquids at a small value of the equilibrium swelling (Q 50 %) and in the case of the absence of significant effect of a solvent (or plasticizer) on the microphase segregation in the material. In this case, the law of normal sorption of a liquid by a crosslinked polymer is keep on. CONCLUSIONS 1. The effect of the thermodynamic quality of solvent on the swelling kinetics of elastomeric polymer networks was theoretically and experimentally studied. Swelling is considered as a set of interrelated processes of diffusion and strain of a material. It is shown that the quality of a solvent, estimated by the Flory-Huggins parameter value, significantly affects the nature of kinetic curves of polymer network swelling. 2. It was found that swelling curves are S-shaped ones for values of the Flory-Huggins parameter less than 0.5. Swelling is described by the law of normal sorption in poor solvents. 3. It was shown that the determination of the diffusion coefficient was to carry on the final stage of the swelling kinetic curve, which was described by a universal asymptotic expression [6.6.6]. The initial stage of the kinetic curve for this is of little use, because it is not possible to obtain a sufficiently accurate and simple analytical expression. 4. It was found that increase in solubility of a liquid in polymer had a positive effect on the diffusion coefficient of the solvent under swelling of crosslinked elastomer therein. REFERENCES 1. 2. 3. 4. 5. 6. 7.
E.Ya. Denisyuk, V.V. Tereshatov, Appl. Mechanics Techn. Phys., 38, 113 (1997). E.Ya. Denisyuk, V.V. Tereshatov, Vysokomolek. Soed., 42A, 71 (2000). E.Ya. Denisyuk, V.V. Tereshatov, Vysokomolek. Soed., 42A, 2130 (2000). T. Tanaka, D. Fillmore, J. Chem. Phys., 70, 1214 (1979). A. Peters, S.J. Candau, Macromolecules, 21, 2278 (1988). Y. Li, T. Tanaka, J. Chem. Phys., 92, 1365 (1990). A.Ya. Malkin, A.E. Chalykh, Diffusion and Viscosity of Polymers. Methods of determination (In Russian). Chemistry, Moscow, 1979. 8. E.Ya. Denisyuk, E.R. Volkova, Polym. Sci., 45A, 686 (2003). 9. E.N. Tereshatova, V.V. Tereshatov, V.P. Begishev, M.A. Makarova, Vysokomolek. Soed, 34B, 22(1992). 10. V.V. Tereshatov, V.Yu. Senichev, Influence of structure on equilibrium swelling. In Handbook of Plasticizers, ChemTec Publishing, Toronto, 2005. 11. P.J. Flory, Principles of Polymer Chemistry, Cornell Univ. Press, Ithaca, 1953. 12. V.V. Tereshatov, E.R. Volkova, E.Ya. Denisyuk, Plastmassy, 13, No.12, 14 (2004)
Swelling 6.1 MODERN VIEWS ON KINETICS OF SWELLING OF CROSSLINKED ELASTOMERS IN SOLVENTS E. Ya. Denisyuk and V. V. Tereshatov Institute of Continuous Media Mechanics and Institute of Technical Chemistry, Ural Branch of Russian Academy of Sciences, Perm, Russia
6.1.1 INTRODUCTION Diffusion phenomena encountered in mass-transfer of low-molecular liquids play an important role in many technological processes of polymer manufacture, processing, and use of polymeric materials. Diffusion of organic solvents in crosslinked elastomers may cause considerable material swelling. In this case, the polymeric matrix experiences strains as large as several hundred percent, while a non-homogeneous distribution of a liquid caused by diffusion results in establishing stress-strain state capable of affecting the diffusion kinetics. The processes of material deformation and liquid diffusion in such systems are interrelated and nonlinear in nature and are strongly dependent on physical and geometrical nonlinearities. Therefore, exact relations of nonlinear mechanics of elasticdeformable continuum are the mainstream of a sequential theory of mass-transfer processes of low-molecular liquids in elastomers. The general principles of the development of nonlinear models of mass transfer in elastically deformed materials were developed in previous studies.1,2 The general formulation of constitutive equations and the use of non-traditional thermodynamic parameters such as partial stress tensors and diffusion forces lead to significant difficulties in attempts to apply the theory to the description of specific systems.3,4 Probably, because of this, the theory is little used for the solution of applied problems. In the paper,5 a theory for mechanical and diffusional processes in hyperelastic materials was formulated in terms of the global stress tensor and chemical potentials. The approach described in1,2 was used as the basic principle and was generalized to the case of a multi-component mixture. An important feature of the work5 is that, due to the structure of constitutive equations, the general model can be used without difficulty to describe specific systems. In the paper6 the nonlinear theory5 was applied to steady swelling processes of crosslinked elastomers in solvents. The analytical and numerical treatment reveals three possible mechano-diffusion modes which differ qualitatively. Self-similar solutions obtained for these modes describe asymptotic properties at the initial stage of swelling. These
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6.1 Modern views on kinetics of swelling of crosslinked elastomers in solvents
modes are related to thermodynamic material properties. The theoretical predictions have been verified in the experiments conducted on real elastomers. 6.1.2 FORMULATION OF SWELLING FOR A PLANE ELASTOMER LAYER Consider an infinite plane elastomer layer of thickness 2h embedded in a low-molecular liquid. Suppose that the elastomer initially does not contain liquid and it is not strained. This state is taken as a reference configuration. Let us introduce the Cartesian coordinates (x,y,z) with the origin placed in the layer center and relate them to a polymer matrix. In the examined problem, the Cartesian coordinates will be used as the material coordinates. With reference to the layer, the x axis has a transverse direction and the other axes have longitudinal directions. In our approach, we define the problem under consideration as a one-dimensional problem, in which all quantities characterizing the elastomer state depend only on the x-coordinate. On swelling, the layer experiences transversal and longitudinal deformations which can be written as X = X(x,t) Y = (t)y Z = (t)z
[6.1.1]
where (X,Y,Z) are the spatial Cartesian coordinates specifying the actual configuration of the polymeric matrix. From this it follows that the relative longitudinal stretch of the layer is 2 = 3 = t and the relative transversal stretch is 1 = x t = X x . The quantity J = 1 2 3 =
2
[6.1.2]
characterizes a local relative change in the material volume due to liquid absorption. The boundary conditions and the relations describing free swelling of the plane layer in the reference configuration are represented in5 as N N ---------1- = ------ D ---------1- N 1 = N 1 x t x x t
[6.1.3]
N 2 t = 0
[6.1.4]
1 x = 0
[6.1.5]
N 1 x 0 = 0
[6.1.6]
N 1 0 t x = 0 X 0 t = 0
[6.1.7]
h t = 0 1 h t = 0
[6.1.8]
2 x t = 3 x t = 0
[6.1.9]
where: N1,N2 μ
the molar concentrations of the liquid and the chains of polymeric network of elastomer, respectively, the chemical potential of the liquid dissolved in material
E. Ya. Denisyuk and V. V. Tereshatov k
295
(k = 1,2,3) are the principal values of the Piola stress tensors.
The angular brackets denote integration with respect to coordinate x: = h
–1
h
dx 0
Because of a symmetry of the swelling process in a layer, the problem is solved for 0
–1
[6.1.10]
where the volume fraction of the polymer is = N2 V2 N1 V1 + N2 V2
[6.1.11]
where: V1 and V2 the molar volumes of liquid and chains of the elastomer network, respectively
To make the definition of the examined problem complete, we need to add to the above model equations, the constitutive relations for mechanical stress tensor and chemical potential of a liquid. According to5,6 this the equations are given by –1
–1
–1
k = RTV 2 k – I 1 k 3 – pJ k –1 1 3
= mix + RTZ
1 3 + V1 p 2
mix = RT ln 1 – + + where: R T
the gas constant per mole the absolute temperature
[6.1.12] [6.1.13] [6.1.14]
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6.1 Modern views on kinetics of swelling of crosslinked elastomers in solvents μmix p Z
the chemical potential of mixing pressure the Flory-Huggins interaction parameter = V2/V1
I1
= 1 + 2 + 3
1
I1/J2/3
2
2
2
The above equations follow from the classical elasticity theory and the Flory theory of polymeric networks.7 From Eq. [6.1.5] and the second condition of Eq. [6.1.8], we find that 1(x,t) = 0. This equation together with Eq. [6.1.12] yields the expression for pressure. By substituting it in the formulas for chemical potential [6.1.13] and longitudinal stresses, we find, using Eqs. [6.1.2] and [6.1.10], that –1
2
5
[6.1.15]
4
[6.1.16]
2 = 3 = RTV 2 – J –1
= mix 1 J + RTZ J
A substitution of Eq. [6.1.15] in Eq. [6.1.9] gives an expression for longitudinal stretch of the layer 6
2
= J x t
[6.1.17]
With consideration of Eq. [6.1.16], the boundary condition at x = h is transformed to –1
4
mix 1 J RT + Z J = 0
[6.1.18]
Thus, the initial swelling problem for a plane layer is reduced to a boundary value problem for diffusion equation [6.1.3] with boundary conditions of Eqs. [6.1.6], [6.1.7], [6.1.17] and [6.1.18]. The solution to this problem provides a full description of swelling processes in the plane layer. In other words, using Eqs. [6.1.1], [6.1.2], [6.1.10] and [6.1.15] we can define a current distribution of a liquid through the layer and calculate the stress-strain state of the material. It should be noted that boundary conditions of Eq. [6.1.18] and Eq. [6.1.17] specify the existence of positive feedback in the system, which is responsible for the onset of unsteady boundary regime during material swelling. The nonlinear distributed systems with positive feedback are generally known as active media and are distinguished for their complex and multimode response.8 In free swelling, the response of elastomers is, in a sense, similar to that of active media. Such behavior is most pronounced when the extent of material swelling is high, which makes this case worthwhile for detailed investigation. For high-swelling elastomers, the volume fraction of polymer in equilibrium swelling state denoted in the following as and the volume fraction of polymer at the elastomer-liquid interface = 1/J entering Eq. [6.1.18] are small quantities. The asymptotic behavior of the function μ( ) at 0 is described by RT = – b
[6.1.19]
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297
The constants b and a can be calculated using the Flory equation [6.1.14]. A second order expansion of ln(1 ) as a power series of gives b = 1/2 and = 2. The scaling approach gives a slightly different value of , which is found to be = 9/4 (des Cloizeaux law9). A volume fraction of the polymer in equilibrium swelling state can be determined by substituting Eq. [6.1.19] in Eq. 6.1.18] and setting = J-1 = and -1/3, yields – 3 3 – 1 bZ . Then, using Eqs. [6.1.18], [6.1.19] and the last relation, we arrive at the following expression for the volumetric swelling ratio of the layer at the elastomer-liquid interface: –1
J
13
6d
[6.1.20]
where 2 d = --------------------3 + 1
[6.1.21]
Note that approximate Eq. [6.1.20] defines the strain dependence of the equilibrium swell ratio of the elastomer in a liquid medium under conditions of biaxial symmetric material extension. Substituting Eq. [6.1.17] in Eq. [6.1.20], we express the boundary swell ratio in terms of liquid distribution in the layer J h t =
2d – 1
2
J x t
d
[6.1.22]
Then the problem is finally defined as u t = k u I u x x ; x 0 1 , t > 0
[6.1.23]
u x 0 = 0 u x 1 t = 0
[6.1.24] 2 d
1 – u 0 t + = 1 – u x t +
[6.1.25]
Here we assign dimensions to the variables. The quantities h and h2/D0 (where D0 is the value of diffusion coefficient in the state of ultimate elastomer swelling) are used as the units of distance and time. For the sake of convenience we transform, the coordinate to x 1 – x . Integrating for x between the limits from 0 to 1 in Eq. [6.1.25] is designated by angular brackets. The function u(x, t) takes the value over the interval (0, 1) and represents a dimensionless concentration of penetrating liquid. It is related to the liquid concentration and local material swelling by the following equations: N1 = V1
–1
–1
– 1 u x t J x t = 1 – u x t +
[6.1.26]
The quantity l = represents the longitudinal layer stretch normalized to unity. By virtue of [6.1.17] and [6.1.26] we may write 6
2
I t = 1 – u x t +
[6.1.27]
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6.1 Modern views on kinetics of swelling of crosslinked elastomers in solvents
Dimensionless diffusion coefficient is defined by the formula k(u, l) = D(u, l)/D0. The longitudinal stresses in the layer (15) are expressed in terms of dimensionless stresses q(x, t) by –1
2 = 3 = RTV 2 q x t
[6.1.28]
where according to Eqs. [6.1.15] and [6.1.27] q x t =
–1 3
2
6
t 1 – 1 – u x t + I t
[6.1.29]
Consider two functions 2
g 1 t = u x t g 2 t = u x t
[6.1.30]
which are integral characteristics of swelling kinetics for a plane layer and can be determined from experiments. The first function characterizes a relative amount of liquid absorbed by a polymer in time t and the second function according to Eq. [6.1.27] is related to longitudinal layer deformation. For high-swelling elastomers 6
g2 t I t
[6.1.31]
The numerical results obtained by solving model problem of Eqs. [6.1.23] [6.1.25] for a constant diffusion coefficient are plotted in Figure 6.1.1.6 The obtained curves show the evolution of penetrating liquid concentration and longitudinal stresses. It is seen that the boundary liquid concentration during swelling monotonically increases.
Figure 6.1.1. Distribution of penetrating liquid (a) and longitudinal stresses (b) during swelling of a plane layer with constant diffusion coefficient k(u, l) = 1 at = 0.1 and d = 2/9: 1 t = 0.05; 2 t = 0.2; 3 t = 0.4; 4 t = 0.6; 5 t = 1; 6 t = 1.8. [Adapted, by permission, from E. Ya. Denisyuk, V. V. Tereshatov, Vysokomol. soed., A42, 74 (2000)].
6.1.3 DIFFUSION KINETICS OF PLANE LAYER SWELLING Consider two stages of swelling process in a plane layer the initial and final. In the initial stage, the influence of the opposite layer boundary on the swelling process is non-essential
E. Ya. Denisyuk and V. V. Tereshatov
299
and therefore diffusion in a layer of finite thickness at sufficiently small values of time can be considered as the diffusion in half-space. At the very beginning of the swelling process the amount of absorbed liquid is rather small. Hence, we may set u x t 0 in the right-hand side of Eqs. [6.1.25] and [6.1.27] which results in u 0 t 0 =
2d
– 1 – I t
13
and Eq. [6.1.23] becomes an usual parabolic equation describing diffusion on a half-line with constant boundary concentration 0. It has self-similar solution of the form u(x,t)= 0(x/t1/2). The function satisfies the equation (k()' + ' /2 = 0 and the boundary conditions 0 = 1 + = 0
[6.1.32]
From this follows the expression for the integral process characteristics g1 t = 0 M1 t
12
2
g2 t = 0 M2 t
12
where
Mp =
p
d p = 1 2
[6.1.33]
0
These relations define the asymptotic properties of swelling at t 0 . As more and more liquid is absorbed, the longitudinal strains in the layer increase. By virtue of Eq. [6.1.25], this causes the growth of liquid concentration at the boundary. For high-swelling materials at sufficiently large values of time, all terms in Eq. [6.1.25] involving as a multiplier factor can be neglected to the first approximation. The resulting expression is written as 2
u 0 t = u x t
d
[6.1.34]
where the angular brackets denote integrating for x in the limits from 0 to + . Since for arbitrary dependence of k(u,l) a boundary-value solution of equation [6.1.23] on the half-line with boundary condition of Eq. [6.1.34] cannot be represented in a similar form, we restrict our consideration to a model problem with diffusion coefficients defined by s
[6.1.35]
s 6p
[6.1.36]
k u I = u s 0 k u I = u I s 0 p 0
(Let us assume that s = 0 corresponds to a constant diffusion coefficient k(u, l) = 1). The analysis of this problem allows us to qualitatively explain many mechanisms of diffusion kinetics of elastomer swelling.
300
6.1 Modern views on kinetics of swelling of crosslinked elastomers in solvents
First, consider the diffusion coefficient defined by Eq. [6.1.35]. In this case, Eq. [6.1.23] on the half-line has a variety of self-similar solutions, which can be written as u x t = t x t
[6.1.37]
where the function satisfies conditions of Eq. [6.1.32] and defines the profile of the diffusion wave, (t) describes boundary conditions and (t) function specifies the penetration depth of diffusion wave. Eq. [6.1.37] satisfies the boundary condition of Eq. [6.1.34] and Eq. [6.1.23] on the half-line with the diffusion coefficient of Eq. [6.1.35] in the following cases: 1) (t), (t) are the functions of power type (power swelling mode); 2) (t), (t) are the functions exponentially depending on time (exponential swelling mode); 3) (t) ~ (t0 t)m, (t)~(t0 - t)n, where m, n < 0 (blow-up swelling mode). Power swelling mode occurs at sufficiently small values of s. In this case, the amount of absorbed liquid, boundary concentration, the depth of diffusion wave penetration and the longitudinal layer deformation are the power function of time. If the parameter s approaches the critical value sc = 2 d – 4
[6.1.38]
Swelling process is governed by exponential law. And finally, if s > sc, the swelling mode is of a blow-up nature. The solutions describing these modes are given below. I. Power mode (s < sc): ms n
2m m
u x t = M 2 t = x M 2 t 2q – 1 q
g1 t = M1 M2
[6.1.39]
ms r
t g2 t = M2 t
[6.1.40]
1 1d–2 1d–1 1 m = ------------ n = ------------------- q = ------------------- r = -------------------sc – s sc – s sc – s d sc – s
[6.1.41]
II. Exponential mode (s = sc): 2
2
u x t = exp M 2 t – t 0 = xM 2 exp s c M 2 t – t 0 2 2
g 1 t = M 1 M 2 exp s c 2 + 1 M 2 t – t 0 2
g 2 t = exp s c 2 + 1 M 2 t – t 0 III. Blow-up mode (s > sc): 2m
ms
u x t = M 2 t 0 – t = x M 2 t 0 – t 2q – 1
g1 t = M1 M2
q
2r
t0 – t g2 t = M2 t0 – t
r
where the exponents are defined by Eqs. [6.1.41] but if s > sc, then m, n, q, r < 0.
E. Ya. Denisyuk and V. V. Tereshatov
301
For power and blow-up swelling modes, is derived from the equation s ' ' + n ' – m = 0 . For an exponential mode, this equation will be valid if we put n = sc/2 and m = 1. The constants M1 and M2 are evaluated from Eq. [6.1.33] and the constant t0 can be estimated by the order of magnitude from the condition 2d –2 u 0 t 0 0 . For the exponential mode, we have t0 ~ 2dM 2 ln , and for the – 2 2d m blow-up mode, t0 ~ M 2 . It is worth noting that at m = 1/s, which holds only if s = 1/d 2, solution of Eq. [6.1.39] is expressed in terms of primary functions and describes the diffusion wave propagating with a constant velocity d: u x t = 1 – 2d
1s
dt – x
1s
The solution describing the blow-up mode turns into infinity at the finite time. In the global sense the boundary-value problems admitting such solutions are time unsolvable and are generally applied to modeling high rate physical-chemical processes.10 It is quite evident that all solutions to the swelling problem for a layer of finite thick are limited and each of the self-similar solutions presented in this study describes asymptotic properties of diffusion modes at initial well-developed stage of swelling. At the final swelling stage u x t 1 , an approximate solution to the problem can be obtained by its linearization in the vicinity of equilibrium u = 1. To this end, one needs to introduce a variable v(x, t) = 1 u(x, t). After transformation we get v t = v xx v x 1 t = 0 v 0 t = 2d v x t By making use of the method of variable separation, we find v x t =
2
ak exp –k t cos k 1 – x
[6.1.42]
k=1
where the values of k are determined from the equation k = 2d tan k
[6.1.43]
Restricting ourselves to the first term of a series Eq. [6.1.42], we can write for the final swelling stage the equation of kinetic curve 2
g 1 t = 1 – a 1 1 exp – 1 t sin k
[6.1.44]
The above expressions allow us to describe the shape of kinetic curves g1(t) in general terms. In particular, as it follows from Eqs. [6.1.39] [6.1.41] at q < 1, the kinetic curves in the coordinates (t,g1) are upward convex and have the shape typical for pseudonormal sorption. This takes place at s < sc/2 1. If s = sc/2 1, then q = 1, which corresponds to a linear mode of liquid absorption. At s > sc/2 1 the lower part of the kinetic curve is convex in a downward direction and the whole curve becomes S-shaped. Note that in terms of coordinates (t1/2,g1) at s 0 all the kinetic curves are S-shaped. Hence, the
302
6.1 Modern views on kinetics of swelling of crosslinked elastomers in solvents
Figure 6.1.2. Diffusion kinetics of plane layer swelling for diffusion coefficient k(u) = us at = 0.1 and d = 2/9; a, b are power swelling modes at s = 1 and s = 2.5, respectively; c exponential swelling mode (s = 5); d blow-up swelling mode (s = 5.5). Numerals over curves denote correspond to instants of time. [Adapted, by permission, from E. Ya. Denisyuk, V. V. Tereshatov, Vysokomol. soed., A42, 74 (2000)].
obtained solutions enable us to describe different anomalies of sorption kinetics observed in the experiments on elastomer swelling in low-molecular liquids. Figure 6.1.26 gives the results of numerical solution to problems of Eq. [6.1.25] with diffusion coefficient defined by Eq. [6.1.35]. The kinetic curves of swelling at different values of s are depicted in Figure 6.1.3.6 Here it can be noted that strain dependence of the diffusion coefficient described by Eq. [6.1.36] does not initiate new diffusion modes. The obtained three self-similar solu-
E. Ya. Denisyuk and V. V. Tereshatov
303
Figure 6.1.3. Kinetic curves of plane layer swelling at different values of concentration dependence of diffusion coefficient ( = 0.1,d = 2/9): a power law mode (1 s = 0; 2 s = 1; 3 s = 1.5; 4 s = 2.5); b exponential (5 s = 5) and blow-up mode (6 s = 5.5). [Adapted, by permission, from E. Ya. Denisyuk, V. V. Tereshatov, Vysokomol. soed., A42, 74 (2000)].
tions hold true. Only critical value sc is variable and it is defined by expression s c = 2 – p d – 4 . This fact can be supported by a direct check of the solutions. 6.1.4 EXPERIMENTAL STUDY OF ELASTOMER SWELLING KINETICS The obtained solutions can be applied to experimental study of the diffusive and thermodynamic properties of elastomers. In particular, with the relation s = 2 d – 4 – 1 d – 1 q
[6.1.45]
following from Eqs. [6.1.38] and [6.1.41] we can estimate the concentration dependence of the diffusion coefficient of a liquid fraction in elastomer. According to Eq. [6.1.40] the parameter q is determined from the initial section of the kinetic swelling curve. Experimental estimates of the parameter r can be obtained from the strain curve l(t) using Eqs. [6.1.31] and [6.1.40]. Then by making use of the formula d =1 q/r
[6.1.46]
following from Eq. [6.1.41] we can evaluate the parameter d which characterizes the strain dependence of the equilibrium swelling ratio of elastomer under symmetric biaxial extension in Eq. [6.1.45]. Generally the estimation of this parameter in tests on equilibrium swelling of strained specimens proves to be a tedious experimental procedure. The value of diffusion coefficient in an equilibrium swelling state can be determined from the final section of kinetic swelling curve using Eq. [6.1.44], which is expressed in terms of dimensional variables as 2
2
g 1 t = 1 – C exp – 1 D 0 t h
[6.1.47]
where 1 is calculated from Eq. [6.1.43). For d = 2/9, 1 1.222 . Note that all these relations are valid only for sufficiently high values of elastomer swelling ratio.
304
6.1 Modern views on kinetics of swelling of crosslinked elastomers in solvents
Figure 6.1.4. Kinetic (a) and strain (b) curves of elastomer swelling in toluene: 1 PBU-3; 2 PBU-4; 3 PBU-1; 4 PBU-2. [Adapted, by permission, from E. Ya. Denisyuk, V. V. Tereshatov, Vysokomol. soed., A42, 74 (2000)].
The obtained theoretical predictions have been verified in experiments on real elastomers. The elastomers tested in our experiments were amorphous polybutadiene urethanes (PBU) with polymer network of different density: 0.3 kmol/m3 (PBU-1), 0.05 kmol/m3 (PBU-2), 0.2 kmol/m3 (PBU-3), 0.1 kmol/m3 (PBU-4). Oligooxypropylene triol Laprol 373 was used as a crosslinking agent for curing of prepolymer of oligobutadiene diol. The elastomer specimens were manufactured in the form of disks, 35 mm in diameter, and 2 mm thick. The kinetics of specimen swelling was determined in low-molecular liquids: toluene, dibutyl sebacate (DBS), dioctyl sebacate (DOS). The typical kinetic and strain curves of free swelling are given in Figure 6.1.4.6 The S-shape of the kinetic swelling curves in terms of coordinates (t1/2, g1) is indicative of abnormal sorption. The values of parameters q and r were obtained from kinetic and strain curves using the regression method. The values of correlation coefficient were 0.997 0.999 and 0.994 0.998 respectively. The obtained data and Eqs. [6.1.45], [6.1.46] were then used to calculate s and d. The diffusion coefficients were defined by the kinetic curves in terms of Eq. [6.1.47] under the assumption that d = 2/9. The obtained results were summarized in Table 6.1.1.6 The analysis of these data shows that swelling of the examined elastomers is of power-mode type. The concentration dependence of the liquid diffusion coefficient defined by the parameter s is found to be rather weak. For elastomers under consideration no exponential or blow-up swelling modes have been observed. Table 6.1.1. Experimental characteristics of elastomer swelling kinetics6
q
r
s
d
D0, cm2/s
PBU-1/toluene
0.278
0.68
0.84
0
0.19
1.4×10-6
PBU-2/toluene
0.093
0.83
1.09
0.8
0.24
4.9×10-7
PBU-3/toluene
0.230
0.78
1.02
0.5
0.24
1.3×10-6
PBU-4/toluene
0.179
0.71
0.97
0
0.27
1.4×10-6
PBU-1/DBS
0.345
0.67
0.92
0
0.27
6.2×10-8
Elastomer/Liquid
E. Ya. Denisyuk and V. V. Tereshatov
305
Table 6.1.1. Experimental characteristics of elastomer swelling kinetics6
q
r
s
d
D0, cm2/s
PBU-2/DBS
0.128
0.78
1.04
0.5
0.25
2.5×10-8
PBU-3/DBS
0.316
0.67
0.83
0
0.19
6.6×10-8
PBU-4/DBS
0.267
0.69
0.88
0
0.21
7.4×10-8
PBU-1/DOS
0.461
0.67
0.81
0
0.17
1.8×10-8
PBU-4/DOS
0.318
0.63
0.81
0
0.22
3.4×10-8
Elastomer/Liquid
It is of interest to note that experimental values of the parameter d characterizing the strain dependence of equilibrium swelling ratio for elastomers subjected to uniform biaxial extension closely approximate the theoretical values. It will be recalled that this parameter is specified by Eq. [6.1.21]. Moreover, the Flory theory defines it as d = 2/9 = 0.22(2), whereas the des Cloizeaux law provides d 0.205 , which suggests that the proposed model of elastomer swelling performs fairly well. 6.1.5 CONCLUSIONS In this section, we have developed a geometrically and physically nonlinear model of swelling processes for an infinite plane elastomeric layer and obtained approximate solutions describing different stages of swelling at large deformations of a polymeric matrix. We have identified the strain-stress state of the material caused by diffusion processes and analyzed its influence on the swelling kinetics. It has been found that a non-stationary boundary regime initiated by deformations arising in elastomer during swelling and increasing a thermodynamical compatibility of elastomer with a liquid is the main reason for swelling anomalies observed in the experiments. Anomalies of sorption kinetics turn out to be a typical phenomenon observable to one or another extent in elastic swelling materials. The theory predicts the possibility for qualitatively different diffusion modes of free swelling. A particular mode is specified by a complex of mechanical, thermodynamical, and diffusion material properties. The results of analytical and numerical solutions for a plane elastomer layer show that the swelling process may be governed by three different laws resulting in the power, exponential, and blow-up swelling modes. Experimentally it has been determined that in the examined elastomers the swelling mode is governed by the power law. The existence of exponential and blow-up swelling modes in real materials is still an open question. New methods have been proposed, which allow one to estimate the concentration dependence of liquid diffusion in elastomer and strain dependence of equilibrium swelling ratio under conditions of symmetric biaxial elastomer extension in terms of kinetic and strain curves of swelling. REFERENCES 1 2 3 4
A E Green, P M Naghdi, Int. J. Eng. Sci., 3, 231 (1965). A E Green, T R Steel, Int. J. Eng. Sci., 4, 483 (1966). K R Rajagopal, A S Wineman, MV Gandhi, Int. J. Eng. Sci., 24, 1453 (1986). M V Gandhi, K R Rajagopal, AS Wineman, Int. J. Eng. Sci., 25, 1441 (1987).
306 5 6 7 8 9 10
6.1 Modern views on kinetics of swelling of crosslinked elastomers in solvents E Ya Denisyuk, V V Tereshatov, Appl. Mech. Tech. Phys., 38, 913 (1997). E Ya Denisyuk, V V Tereshatov, Vysokomol. soed., A42, 74 (2000) (in Russian). P J Flory, Principles of polymer chemistry, Cornell Univ. Press, New York, 1953. V A Vasilyev, Yu M Romanovskiy, V G Yahno, Autowave Processes, Nauka, Moscow, 1987 (in Russian). P G De Gennes, Scaling Concepts in Polymer Physics, Cornell Univ. Press, Ithaca, 1980. A A Samarskiy, V A Galaktionov, S P Kurdyumov, A P Mikhaylov, Blow-up Modes in Problems for Quasilinear Parabolic Equations, Nauka, Moscow, 1987 (in Russian)
Vasiliy V. Tereshatov, Valery Yu. Senichev, and E. Ya Denisyuk
307
6.2 EQUILIBRIUM SWELLING IN BINARY SOLVENTS Vasiliy V. Tereshatov, Valery Yu. Senichev, and E. Ya Denisyuk Institute of Continuous Media Mechanics and Institute of Technical Chemistry, Ural Branch of Russian Academy of Sciences, Perm, Russia Depending on the purposes and operating conditions of polymer material processing, the differing demands regarding solubility of low-molecular-mass liquids in polymers exist. Polymeric products designed for use in contact with solvents should be stable against adsorption of these liquids. On the contrary, the well dissolving polymer solvents are necessary to produce polymer films. The indispensable condition of creation of the plasticized polymer systems (for example, rubbers) is the high thermodynamic compatibility of plasticizers with the polymer matrix. Hence, it immediately follows the statement of the problem of regulation of thermodynamic compatibility of polymers with low-molecular-mass liquids in a wide range of its concentration in polymer material. The problem of compatibility of crosslinked elastomers with mixed plasticizers and volatile solvents is thus of special interest. Depending on ratios between solubility parameters of solvent 1, 1, solvent 2, 2, and polymer, 3, solvents can be distinguished as “symmetric” liquids and “non-symmetric” ones. The non-symmetric liquids are defined as a mixture of two solvents of variable composition, solubility parameters 1 and 2 which are larger or smaller than solubility parameter of polymer (2 > 1 > 3, 3 > 2 > 1). The symmetric liquid (SL) with relation to polymer is the mixture of two solvents, whose solubility parameter, 1, is smaller, and parameter, 2, is larger than the solubility parameter of polymer, 3. The dependence of equilibrium swelling on the non-symmetric liquid composition does not have a maximum, as a rule.1 Research on swelling of crosslinked elastomers in SL is of particular interest in the regulation of thermodynamic compatibility of network polymers and binary liquids. Swelling in such liquids is characterized by the presence of maximum on the curve of dependence of network polymer equilibrium swelling and composition of a liquid phase.2,3 The extreme swelling of crosslinked polymers of different polarity in SL was discussed elsewhere.3 The following elastomers were used as samples: a crosslinked elastomer of ethylene-propylene rubber SCEPT-40 [3 = 16 (MJ/m3)1/2, (ve/ V0)x = 0.24 kmol/m3], crosslinked polyester urethane, PEU, from copolymer of propylene oxide and trimethylol propane [3 = 18.3 (MJ/m3)1/2, (ve/V0)x = 0.27 kmol/m3], crosslinked polybutadiene urethane, PBU, from oligobutadiene diol [3 = 17.8 (MJ/m3)1/2, (ve/ V0)x = 0.07 kmol/m3] and crosslinked elastomer of butadiene-nitrile rubber [3 = 19 (MJ/ m3)1/2, (ve/V0)x = 0.05 kmol/m3]. The samples of crosslinked elastomers were swollen to equilibrium at 25oC in 11 SLs containing solvents of different polarity. The following regularities were established. With decrease in the solubility parameter value of component 1 (see Table 6.2.1) in SL (1 < 3), the maximum value of equilibrium swelling, Q, shifts to the field of larger concentration of component 2 in the mixture (Figures 6.2.1 and 6.2.2). On the contrary, with decrease in the solubility parameter 2 (see Table 6.2.1) of components 2 (2 > 3), the
308
6.2 Equilibrium swelling in binary solvents
Figure 6.2.1. Dependence of equilibrium swelling of PEU on the acetone concentration in the mixtures: 1 toluene-acetone, 2 cyclohexane-acetone, 3 heptane-acetone. [Adapted, by permission, from V. V. Tereshatov, M. I. Balashova, A. I. Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch of AS USSR Press, Sverdlovsk, 1989, p. 3.]
Figure 6.2.2. Dependence of equilibrium swelling of PBU on the DBP (component 2) concentration in the mixtures: 1 DOS-DBP, 2 TO-DBP, 3 decaneDBP. [Adapted, by permission, from V. V. Tereshatov, M. I. Balashova, A. I. Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch of AS USSR Press, Sverdlovsk, 1989, p. 3.]
maximum Q corresponds to composition of the liquid phase enriched by component 1 (Figure 6.2.3). Table 6.2.1. Characteristics of solvents and plasticizers at 298K. [Adapted, by permission, from V. V. Tereshatov, M. I. Balashova, A. I. Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch of AS USSR Press, Sverdlovsk, 1989, p. 3.] , kg/m3
V×106, m3
, (MJ/m3)1/2
Cyclohexane
779
109
16.8
Heptane
684
147
15.2
Solvent/plasticizer
Decane
730
194
15.8
Toluene
862
106
18.2
1,4-Dioxane
1034
86
20.5
Acetone
791
74
20.5
Ethyl acetate
901
98
18.6
Amyl acetate
938
148
17.3
Dibutyl phthalate
1045
266
19.0
Vasiliy V. Tereshatov, Valery Yu. Senichev, and E. Ya Denisyuk
309
Table 6.2.1. Characteristics of solvents and plasticizers at 298K. [Adapted, by permission, from V. V. Tereshatov, M. I. Balashova, A. I. Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch of AS USSR Press, Sverdlovsk, 1989, p. 3.] , kg/m3
V×106, m3
, (MJ/m3)1/2
Dioctyl sebacate
913
467
17.3
Transformer oil
890
296
16.0
Solvent/plasticizer
Figure 6.2.3. Dependence of equilibrium swelling of the crosslinked elastomer SCEPT-40 on the concentration of component 2 in the mixtures: 1 heptane-toluene, 2 heptane-amyl acetate, 3 heptane-ethyl acetate. [Adapted, by permission, from V. V. Tereshatov, M. I. Balashova, A. I. Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch of AS USSR Press, Sverdlovsk, 1989, p. 3.]
Figure 6.2.4. Dependence of equilibrium swelling of the crosslinked elastomer SCN-26 on the concentration of component 2 in the mixtures: 1 toluene-acetone, 2 ethyl acetate-dioxane, 3 ethyl acetateacetone. [Adapted, by permission, from V. V. Tereshatov, M. I. Balashova, A. I. Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch of AS USSR Press, Sverdlovsk, 1989, p. 3.]
Neglecting the change of volume on mixing, the solubility parameter of the mixture of two liquids is represented by: 12 = 1 1 + 2 2 where:
1 and 2 volume fractions of components 1 and 2
More exact evaluation of the 12 value is possible if the experimental data on enthalpy of mixing, H, of components of SL are taken into account:4
310
6.2 Equilibrium swelling in binary solvents 2
2
12 = 1 1 + 2 2 – H V 12
12
With a change in 1 and 2 parameters, the SL composition has the maximum equilibrium swelling which corresponds to shifts in the field of composition of the liquid phase. The 12 parameter is close or equal to the value of the solubility parameter of polymer. Such a simplified approach to the extreme swelling of polymers in liquid mixtures frequently works very well in practice. If there is a maximum on the curve of swelling in SL, then the swelling has an extreme character (11 cases out of 12) (Figures 6.2.1-6.2.4). The parameter of interaction, 123, between polymer and a two-component liquid can be used as a co-solvency criterion for linear polymers (or criterion of extreme swelling), more general, than the equality (12 = 3):5 123 = 13 1 + 23 2 – 1 2 12 where:
13 and 23 12
[6.2.1]
parameters of interaction of components 1 and 2 with polymer, correspondingly parameter of interaction of components 1and 2 of liquid mixture
In the equation obtained from the fundamental work by Scott,5 mixed solvent is represented as “a uniform liquid” with the variable thermodynamic parameters depending on composition. If the 123 value is considered as a criterion of existence of a maximum of equilibrium swelling of polymer in the mixed solvent, a maximum of Q should corresponds to the minimum of 123. For practical use of Eq. [6.2.2] it is necessary to know parameters 13, 23, and 12. The values 13 and 23 can be determined from the Flory-Rehner equation, using data on swelling of a crosslinked elastomer in individual solvents 1 and 2. The evaluation of the 12 value can be carried out with use of results of the experimental evaluation of vapor pressure, viscosity and other characteristics of a binary mixture.6,7 To raise the forecasting efficiency of prediction force of such criterion as 123 minimum, the amount of performance parameters determined experimentally must be reduced. For this purpose, the following expression for the quality criterion of the mixed solvent (the analogy with expression of the Flory-Huggins parameter for individual solvent-polymer system) is used: V 12 s 2 123 = 123 + ------- – 12 V 12 = V 1 x 1 + V 2 x 2 RT 3
[6.2.2]
where: V12 V1, V2 x1, x2 R T s 123
molar volume of the liquid mixture molar volumes of components 1 and 2 molar fractions of components 1 and 2 in the solvent universal gas constant temperature, K. constant, equal to 0.34 s
s
The values of entropy components of parameters 13 and 23 (essential for quality prediction)8 were taken into account. Using the real values of entropy components of s s interaction parameters 13 and 23 , we have:
Vasiliy V. Tereshatov, Valery Yu. Senichev, and E. Ya Denisyuk
311
V s 2 13 = 13 – -------1- 3 – 1 RT
[6.2.3]
V s 2 23 = 23 – -------2- 3 – 2 RT
[6.2.4]
quality criterion of solvent mixture is represented by:3 V 12 2 s s 123 = 13 1 + 23 2 + ------- 3 – 12 RT
[6.2.5]
The values of parameters 13 and 23 were calculated from the Flory-Rehner equas tion, using data on swelling of crosslinked polymer in individual solvents, the values 13 , s 23 , and 123 were estimated from Eqs. [6.2.3-6.2.5). Then equilibrium swelling of elastomer in SL was calculated from the equation similar to Flory-Rehner equation, considering the mixture as a uniform liquid with parameters 123 and V12 variable in composition. The calculated ratios of components of mixtures, at which the extreme swelling of elastomers is expected, are given in Table 6.2.2. Table 6.2.2. Position of a maximum on the swelling curve of crosslinked elastomers in binary mixtures. [Adapted, by permission, from V. V. Tereshatov, M. I. Balashova, A. I. Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch of AS USSR Press, Sverdlovsk, 1989, p. 3.] Elastomer PEU
PBU
SCN-26
Binary mixture
Components ratio, wt% Calculation
Experiment
toluene-acetone
90/10
90/10
cyclohexanone-acetone
40/60
50/50
heptane-acetone
30/70
25/25
decane-DBP
30/70
30/70
TO-DBP
40/60
40/60
DOS-DBP
60/40
50/50
ethyl acetate-acetone
70/30
70/30
ethyl acetate-acetone
70/30
70/30
ethyl acetate-1,4-dioxane
Results of calculation of the liquid phase composition at maximum swelling of elastomer correlate with the experimental data (see Table 6.2.2). The approach predicts the existence of an extremum on the swelling curve. This increases the forecasting efficiency of the prediction. The application of “approximation of the uniform liquid” (AUL) for prediction of extreme swelling of crosslinked elastomers is proven under condition of coincidence of composition of a two-component solvent in a liquid phase and in the swollen elastomer.
312
6.2 Equilibrium swelling in binary solvents
Results of study of total and selective sorption by crosslinked elastomers of components of SLs are given below.3 Crosslinked PBU [(ve/V0) = 0.20 kmol/m3] and crosslinked elastomer of butadienenitrile rubber SCN-26 [(ve/V0) = 0.07 kmol/m3] were used in this study. The tests were carried out at 25±0.10oC in the following mixtures: n-nonane-tributyl phosphate (TBP), nhexane-dibutyl phthalate (DBP), n-hexane-dibutyl maleate (DBM), and dioctyl sebacate (DOS)-diethyl phthalate (DEP). A crosslinked elastomer SCN-26 was immersed to equilibrate in amyl acetate-dimethyl phthalate mixture. Liquid phase composition was in range of 5 to 10%. A sol-fraction of samples (plates of 0.9×10-2 m diameter and in 0.3×10-2 m thickness) was preliminary extracted with toluene. For high accuracy of the analysis of binary solvent composition, a volatile solvent, hexane, was used as a component of SL in most experiments. Following the attainment of equilibrium swelling, the samples were taken out of SL and held in air until the full evaporation of hexane, that was controlled by constant mass of sample. A content of a nonvolatile component of SL in elastomer was determined by the difference between the amount of liquid in the swollen sample and the amount of hexane evaporated. In the case of SL with nonvolatile components (such as, DBP or DOS) the ratio of SL components in the swollen PBU was determined by the gas-liquid chromatography, for which purpose toluene extract was used. The volume fractions of components 1 and 2 of SL in a liquid phase 1 and 2 were calculated on the basis of their molar ratio and densities 1 and 2. Volume fraction of polymer, 3 , in the swollen sample was calculated from the equation: 1 3 = --------------Qv + 1 where: QV
volume equilibrium swelling of elastomer in SL.
Volume fractions 1 and 2 of components 1 and 2 of low-molecular-mass liquids inside the swollen gel were determined from the equation: i i = ------------- , (i = 1,2) 1 – 3 where:
i
volume fraction of i-component related to the total volume of its low-molecular-mass part (not to the total volume of three-component system)
The results of study of sorption of two-component liquids in PBU and in crosslinked elastomer SCN-26 are shown in Figures 6.2.5-6.2.8, as dependencies of Qv on the volume fraction 2 of component 2 in a liquid phase and on the volume fraction 2 of component 2 of SL that is a part of the swollen gel. The data vividly show that extremum swelling of crosslinked elastomers in SL can be observed in all investigated cases. At the maximum value of Qv, the compositions of SL in the liquid phase and in the swollen elastomer practically coincide ( 2 2 ).
Vasiliy V. Tereshatov, Valery Yu. Senichev, and E. Ya Denisyuk
Figure 6.2.5. Dependence of equilibrium swelling of PBU on the 2 value for DEP in the liquid phase (1) and the 2 value inside the gel (1') swollen in the mixture DOS-DEP.
313
Figure 6.2.6. Dependence of equilibrium swelling of PBU on the 2 value for DEP in the liquid phase (curves 1 and 2) and the 2 value inside the swollen gel (curves 1' and 2') in the mixtures: 1,1'-hexane(1)DBM(2), 2,2'- hexane(1)-DBP(2).
The total sorption can be determined by the total content of the mixed solvent in the swollen skin9 or in the swollen elastic network (these results). The dependencies of Qv on 2 (Figures 6.2.5-6.2.8) reveal the influence of liquid phase composition on the total sorption. The total sorption of the binary solvent by polymer can also be measured by the value of the volume fraction of polymer in the swollen gel9 because the value of 3 is unequally related to the volume fraction of the absorbed liquid, 3 = 1 – 1 + 2 . At the fixed total sorption (Qv or 3 = const) the preferential sorption, e, an be found from the following equation: Figure 6.2.7. Dependence of equilibrium swelling of PBU on the 2 value for TBP in the liquid phase (1) and the 2 value in the gel (1') swollen in the mixture: nonane-TBP.
= 1 – 1 = 2 – 2
314
6.2 Equilibrium swelling in binary solvents
Figure 6.2.8. Dependence of equilibrium swelling of crosslinked elastomer SCN-26 on the 2 value for DMP in the liquid phase (1) and the 2 value in the gel (1'), swollen in the mixture: amyl acetate-DMP.
Figure 6.2.9. Experimental dependence of the preferential sorption on the volume fraction 2 of component 2 in the liquid phase: 1 DOS(1)-DEP(2)PBU(3), 2 hexane(1)-DBP(2)-PBU(3), 3 hexane(1)-DBM(2)-PBU(3), 4 amyl acetate(1)DMP(2)-SCN-26(3), 5 nonane(1)-TBP(2)-PBU(3).
At the same values of Qv difference between coordinates on the abscissa axes of points of the curves 1-1' , 2-2' (Figures 6.2.5-6.2.8) are equal (Figure 6.2.9). As expected,10 preferential sorption was observed, with the essential distinction of molar volumes V1 and V2 of components of the mixed solvent (hexane-DBP, DOS-DEP). For swelling of the crosslinked elastomer SCN-26 in the mixture of components, having similar molar volumes V1 and V2 (e.g., amyl acetate-dimethyl phthalate) the preferential sorption of components of SL is practically absent. Influence of V1 and V2 and the influence of double interaction parameters on the sorption of binary liquids by crosslinked elastomers was examined by the method of mathematical experiment. Therewith the set of equations describing swelling of crosslinked elastomers in binary mixture, similar to the equations obtained by Bristow6 from the Flory-Rehner theory11 and from the work of Schulz and Flory,12 were used: 2
2
2
ln 1 + 1 – I 2 + 12 2 = ln 1 + 1 – I 2 + 3 + 12 2 + 12 3 + + 12 + 13 – I 23 2 3 + e V 3 V 1 3
13
–1
–1
2
2 – --- 3 f
[6.2.6]
–1
ln 2 + 1 – I 1 + 1 12 1 = ln 2 + 1 – I 1 + 3 + –1
2
2
13
+ I 12 1 + I 23 3 + 12 + I 23 – 13 1 3 + e V 3 V 2 3
2 – --- 3 f
[6.2.7]
Vasiliy V. Tereshatov, Valery Yu. Senichev, and E. Ya Denisyuk
315
where: l f
= V1/V2 functionality of a network
The analysis of calculations from Eqs. [6.2.6] and [6.2.7] has shown that if V1 < V2, the preferential sorption is promoted by difference in parameters of interaction, when 12 > 13. The greater is 12 value at V 1 V 2 the more likely preferential sorption takes place with all other parameters being equal. The same applies to the diluted polymer solutions. To improve calculations of the preferential sorption in the diluted solutions of polymers, the correction of Flory's theory is given in works9,13-15 by introduction of the parameter of three-component interaction, T, into the expression for free energy of Figure 6.2.10. Experimental data and calculated depenmixing, and substitution of T by qT.14 This dence of equilibrium fraction of components 1 (1), 2 (2), and 3 (3) in PBU sample swollen in the hexane- approach is an essential advancement in the DBP mixture on the 2 value for DBP in the liquid analysis of a sorption of two-component phase: lines calculation, points experimental. liquids by polymer. On the other hand, the increase in the number of experimental parameters complicates the task of prediction of the preferential sorption. In swelling crosslinked elastomers, the preferential sorption corresponds to the maximum Qv value and compositions in a swollen polymer and a liquid phase practically coincide (Figures 6.2.5-6.2.8). This observation can be successfully used for an approximate evaluation of the preferential sorption. Assuming that and at extremum of the total sorption (min), AUL5 e can be used to calculate the effective value of 12 from the expression for 16 m
13 23 V 1 123 V 1 e - + ------------- – --------------------- 12 = -----m m m m m 2 1 V 2 V 12 1 2
[6.2.8]
where: m e 12
the index for the maximum of sorption. the value, calculated from the equation [6.2.8], substitutes 12 from the Eqs. [6.2.6] and [6.2.7]
The results of calculations are presented as dependencies of volume fractions, 2, and 3 of the triple system components (swollen polymer) vs. the volume fraction 2 (or 1) of the corresponding components of the liquid phase (Figures 6.2.10 and 6.2.11). For practical purposes it is convenient to represent the preferential sorption as the dependence of equilibrium composition of a binary liquid (a part of the swollen gel) vs. composition of the liquid phase. These calculated dependencies (solid lines) and experimental (points)
316
6.2 Equilibrium swelling in binary solvents
Figure 6.2.11. Dependence of equilibrium fraction of components 1 (1), 2 (2), and 3 (3) in SCN-26 sample swollen in the amyl acetate-DMP mixture on the 2 value for DMP in the liquid phase: lines calculation, points experimental.
Figure 6.2.12. Dependence of equilibrium 2 value on the 2 value in the liquid phase: 1 amyl acetate(1)DMP(2)-SCN-26(3), 2 hexane(1)-DBM(2)-PBU(3), 3 nonane(1)-TBP(2)- PBU (3); lines calculation, points experimental.
data for three systems are given in Figure 6.2.12. The results of calculations based on AUL, are in the satisfactory agreement with experimental data. Hence the experimentally determined equality of concentrations of SL components in the swollen gel and in the liquid phase allows one to predict composition of liquid, whereby polymer swelling is at its maximum, and the preferential sorption of components of SL. To refine dependencies of 1 on 1 or 2 on 2, correction can be used, for example, minimization of the square-law deviation of calculated and experimental data on the total sorption of SL by polymer. Thus it is necessary to account for proximity of the compositions of solvent in the swollen gel and the liquid phase. REFERENCES 1 2 3 4 5 6 7 8 9 10 11
A Horta, Makromol. Chem., 182, 1705 (1981). V V Tereshatov, V Yu Senichev, A I Gemuev, Vysokomol. Soedin., 32B, 422 (1990). V V Tereshatov, M I Balashova, A I Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch. of AS USSR Press, Sverdlovsk, 1989, p. 3. A A Askadsky, Yu I Matveev, Chemical structure and physical properties of polymers, Chemistry, Moscow, 1983. R L Scott, J. Chem. Phys., 17, 268 (1949). C M Bristow, Trans. Faraday Soc., 55, 1246 (1959). A Dondos, D Patterson, J. Polym. Sci., A-2, 5, 230 (1967). L N Mizerovsky, L N Vasnyatskaya, G M Smurova, Vysokomol. Soedin., 29A, 1512 (1987). J Pouchly, A Zivny, J. Polym. Sci., 10, 1481 (1972). W R Krigbaum, D K Carpenter, J. Polym. Sci., 14, 241 (1954). P J Flory, J Rehner, J. Chem. Phys., 11, 521 (1943).
Vasiliy V. Tereshatov, Valery Yu. Senichev, and E. Ya Denisyuk 12 13 14 15 16
A R Shulz, P J Flory, J. Polym. Sci., 15, 231 (1955). J Pouchly, A Zivny, J. Polym. Sci., 23, 245 (1968). J Pouchly, A Zivny, Makromol. Chem., 183, 3019 (1982). R M Msegosa, M R Comez-Anton, A Horta, Makromol. Chem., 187, 163 (1986). J Scanlan, J. Appl. Polym. Sci., 9, 241 (1965).
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Vasiliy V. Tereshatov and Valery Yu. Senichev
319
6.3 SWELLING DATA ON CROSSLINKED POLYMERS IN SOLVENTS Vasiliy V. Tereshatov and Valery Yu. Senichev Institute of Technical Chemistry Ural Branch of Russian Academy of Sciences, Perm, Russia Data on equilibrium swelling of selected crosslinked elastomers in different solvents are presented in Table 6.3.2. All data were obtained in the author's laboratory during 5 years of experimental work. The network density values for these elastomers are given in Table 6.3.1. The data can be used for the quantitative evaluation of thermodynamic compatibility of solvents with elastomers and for calculation of Z, the thermodynamic interaction parameter. These data can be recalculated to the network density distinguished by the network density value, given in Table 6.3.1, using Eq. [4.2.9]. Network density values can be used for calculation of the interaction parameter. It should be noted that each rubber has specific ratio for the equilibrium swelling values in various solvents. This can help to identify rubber in polymeric material. Temperature influences swelling (see Subchapter 4.2). Equilibrium swelling data at four different temperatures are given in Table 6.3.3. Polymer samples were made from industrial rubbers. The following polyols were used for preparation of polyurethanes: butadiene diol (M~2000) for PBU, polyoxybutylene glycol (M~1000) for SCU-PFL, polyoxypropylene triol (M~5000) for Laprol 5003, polydiethylene glycol adipate (M~2000) for P-9A and polydiethylene glycol adipate (M~800) for PDA. Polyurethanes from these polyols were synthesized by reaction with 2,4-toluylene diisocyanate with addition of crosslinking agent trimetylol propane, PDUE, synthesized by reaction of oligobutadiene isoprene diol (M~4500) with double excess of 2,4-toluylene diisocyanate, followed by the reaction with glycidol. Table 6.3.1. Network density values for tested elastomers (data obtained from the elasticity modulus of samples swollen in good solvents) Elastomer
Trade mark
Network density, (kmol/m3)×102
Silicone rubber
SCT (1)
6.0
Butyl rubber
BR (2)
8.9
Polybutadiene rubber
SCDL (3)
40.5
Ethylene-propylene rubber
SCEPT (4)
2.7
Isoprene rubber
SCI-NL (5)
8.9
Butadiene-nitrile rubber
SCN-26 (6)
5.1
Polydiene-urethane-epoxide
PDUE (7)
16.0
Polybutadiene urethane
PBU (8)
20.8
Polyoxybutylene glycol urethane
PFU (9)
10.0
320
6.3 Swelling data on crosslinked polymers in solvents
Table 6.3.1. Network density values for tested elastomers (data obtained from the elasticity modulus of samples swollen in good solvents) Elastomer Polyoxypropylene glycol urethane
Trade mark
Network density, (kmol/m3)×102
Laprol 5003 (10)
43.0
Polydiethylene glycol adipate urethane P-9A (11)
6.4
Polydiethylene glycol adipate urethane PDA (12)
9.6
Table 6.3.2 Equilibrium swelling data (wt%) at 25oC. Elastomer number identifies elastomer (see the second column in Table 6.3.1) Solvent\elastomer*
1
2
3
4
5
6
7
8
9
10
11
122
78
16
44
4
137
84
16
42
0
101
32
0
7
139
28
1
155
315
39
24
238
3
53
4
12
Hydrocarbons Pentane
355
75
Hexane
380
305
Heptane
367
357
Isooctane
380
341
Decane
391
Cyclohexane
677
Transformer oil
47
214
105
586
30
881
10
1020 230
1580
600
3 0.5
Toluene
384
1294
435
492
356
134
315
77
31
Benzene
233
511
506
479
359
158
340
175
73
0-Xylene
515
496
356
122
288
53
42
87
2
22
2
41
0.1
Ethers Diamyl
310
Diisoamyl
333
220
889
584
791 120
Diethyl of diethylene glycol
85
1,4-Dioxane
248 33
Didecyl Dioctyl
20
428
180
896
156
702
7
168
11
203
6
242
3
251
23
1 54
264
178
782
48
192
848
133
213
88
317
251
121
64
40
210
238
48
35
249
36
Tetrahydrofuran
Esters of monoacids Heptyl propionate
260
236
Ethyl acetate
20
Butyl acetate
55
304
382
287
55
562
170
Isobutyl acetate
48
267
Amyl acetate
82
343
Isoamyl acetate
74
Heptyl acetate
213
236
100
545
100
Methyl capronate
369
285
115
Isobutyl isobutyrate
328
276
64
22 6 260
36
26
6
6
Vasiliy V. Tereshatov and Valery Yu. Senichev
321
Table 6.3.2 Equilibrium swelling data (wt%) at 25oC. Elastomer number identifies elastomer (see the second column in Table 6.3.1) Solvent\elastomer*
1
2
3
4
5
6
7
8
9
10
11
12
Esters of multifunctional acids Dihexyl oxalate
28
350
73
166
11
9
Diethyl phthalate
6
837
47
93
165
272
496
126
Dibutyl phthalate
9
767
123
154
121
228
47
20
187
9
Dihexyl phthalate
570
Diheptyl phthalate Dioctyl phthalate
37 8
28
189
Dinonyl phthalate
211
181
Didecyl phthalate
1
33
1.4
23
Diamyl maleate
425
Dimethyl adipate
560
Diamyl adipate Dihexyl adipate
197
71
0.5 232
19
14
246
716
6
294
203
88
295
199
42
2
2
126
12
0.6
280
Dioctyl adipate Dipropyl sebacate
8
20
Diamyl sebacate
70
Diheptyl sebacate Dioctyl sebacate
3
29
60 13
160
127
2 118
445
39
Triacetin
34
Tricresyl phosphate
800
Tributyl phosphate
261
162
5.5
15
28
45 300
74
3 0.4
0.7
489
129
256
93
105
327
523
140 244
238
80
Ketones Cyclohexanone Acetone
577 7
44
88
218
99
72
7
12
Alcohols Ethanol
49
Butanol
25
16
Pentanol
28
33
66
10
5
Hexanol
46
34
62
9
4
67
19
Heptanol
36
Nonanol
57
3
Halogen compounds CCl4
2830
284
999
584
Chlorobenzene
234
Chloroform
1565
Fluorobenzene
66 277
114
572
616
205
113
Nitrogen compounds Diethyl aniline
336
Dimethylformamide
52
120
34 918
322
6.3 Swelling data on crosslinked polymers in solvents
Table 6.3.2 Equilibrium swelling data (wt%) at 25oC. Elastomer number identifies elastomer (see the second column in Table 6.3.1) Solvent\elastomer*
1
2
3
4
5
6
7
8
9
10
11
12
277
298
242
377
799
241
Capronitrile
769
142
Acetonitrile
47
69
Nitrobenzene
Aniline
115
84
16
323 317
423
*See Table 6.3.1 for elastomer’s name
Table 6.3.3 Equilibrium swelling data (wt%) at -35, -10, 25, and 50oC Solvent\Elasto mer
Laprol*
SCU-PFL
P-9A
PBU
SCN-26
Isopropanol
8,12,37,305
8,19,72
8,10,18,28
3,5,18,28
20,23,26,41
Pentanol
27,34,80,119
16,25,78,104
7,9,10,18
8,9,33,52
31,37,49,60
Acetone
80,366,381,-
80,122,132,-
48,73,218,-
56,321,347,-
162,254,269,382
Ethyl acetate
214,230,288,314
113,114,133,138
209,210,210,213
165,171,187,257
324,343,395,407
Butyl acetate
294,304,309,469
119,122,123,125
41,44,64,80
288,293,307,473
404,426,518,536
Isobutyl acetate
259,259,288,-
89,92,100,105
23,28,48,57
210,212,223,348
309,326,357,362
Amyl acetate
315,309,315,426
124,136,144,155
16,18,36,44
285,297,298,364
343,347,358,359
Tetrahydrofuran
91,96,97,119
119,177,192,-
838,840,848,859
45,51,57,80
145,150,166,-
o-Xylene
363,368,389,471
117,121,122,137
24,25,53,60
328,357,369,375
428,440,405,406
Chlorobenzene
522,537,562,-
241,242,242,246
238,244,277,333
517,528,559,698
967,973,985,1256
Acetonitrile
19,21,28,33
23,26,39,41
254,263,323,362
6,10,16,27
47,47,47,82
Hexane
50,52,61,75
2,3,9,14
4,4,4,28
51,56,63,80
Toluene
360,366,380, 397
120,122,134,149
50,57,77,85
331,339,372,415
*(ve/V) = 0.149 kmol/m3. Network density values for other elastomers correspond to Table 6.3.2
Vasiliy V. Tereshatov and Valery Yu. Senichev
323
6.4 INFLUENCE OF STRUCTURE ON EQUILIBRIUM SWELLING Vasiliy V. Tereshatov and Valery Yu. Senichev Institute of Technical Chemistry Ural Branch of Russian Academy of Sciences, Perm, Russia Swelling of single-phase elastomers is, with other parameters being equal, limited by the chemical network. Microphase separation of hard and soft blocks can essentially influence swelling of block-copolymers. Hard domains formed in this process are knots of physical network, which can be resistant to action of solvents.1-4 Swelling of polyurethane blockcopolymers with urethane-urea hard segments is investigated. The maximum values of swelling, Qmax, of segmented polyurethane (prepolymer of oligopropylene diol with functional isocyanate groups) cured with 4,4’-methylene-bis-o-chloroaniline (MOCA) are given in Tables 6.4.1 and 6.4.2. The prepolymer Vibratane B 600 was obtained by the reaction of oligopropylene diol with 2,4-toluylene diisocyanate. The swelling experiments were carried out in four groups of solvents of different polarity and chemical structure.5 The effective molecular mass of elastically active chains, Mc, between network crosslinks was estimated from the Flory-Rehner equation.6 The interaction parameter of solvent with polymer was determined by calculation. In the first variant of calculation, a classical method based on the solubility parameter concept, was used with application of Bristow and Watson's semi-empirical relationship for 1:7 V 2 s 1 = 1 + -------1- 1 – p RT where:
s
1 V1 R1 T 1 and p
[6.4.1]
a lattice constant whose value can be taken as 0.34 the molar volume of the solvent the gas constant the absolute temperature the solubility parameters of the solvent and the polymer, respectively
However, to evaluate 1 from Eq. [6.4.1], we need accurate data for 1. In some cases the negative Mc values are obtained (Tables 6.4.1). The reason is that the real values of the entropy component of the 1 parameter can strongly differ from the 0.34 value. Table 6.4.1. Characteristics of polyurethane-solvent systems at 25oC. [Adapted, by permission, from U.S. Aithal, T.M. Aminabhavi, R.H. Balundgi, and S.S. Shukla, JMS - Rev. Macromol. Chem. Phys., 30C (1), 43 (1990).] Penetrant
Qmax
1
Mc
0.378
630
Monocyclic aromatics Benzene
0.71
324
6.4 Influence of structure on equilibrium swelling
Table 6.4.1. Characteristics of polyurethane-solvent systems at 25oC. [Adapted, by permission, from U.S. Aithal, T.M. Aminabhavi, R.H. Balundgi, and S.S. Shukla, JMS - Rev. Macromol. Chem. Phys., 30C (1), 43 (1990).] Penetrant
Qmax
1
Mc
Toluene
0.602
0.454
790
p-Xylene
0.497
0.510
815
Mesitylene
0.402
0.531
704
Chlorobenzene
1.055
0.347
905
Bromobenzene
1.475
0.347
1248
o-Dichlorobenzene
1.314
0.357
1106
Anisole
0.803
0.367
821
Nitrobenzene
1.063
0.356
835
Methanol
0.249
1.925
-90
Aliphatic alcohols Ethanol
0.334
0.349
172
n-Propanol
0.380
0.421
484
Isopropanol
0.238
0.352
249
n-Butanol
0.473
2.702
-131
2-Butanol
0.33
1.652
-307
2-Methyl-1-propanol
0.389
0.440
535
Isoamyl alcohol
0.414
0.357
398
Halogenated aliphatics Chloroform
4.206
0.362
3839
Bromoform
5.583
0.435
4694
1,2-Dibromoethane
1.855
0.412
770
1,3-Dibromopropane
1.552
0.444
870
Dichloromethane
2.104
0.34
1179
Trichloroethylene
1.696
0.364
1098
Tetrachlorethylene
0.832
0.368
429
1,2-Dichlorethane
1.273
0.345
728
Carbon tetrachloride
1.058
0.538
860
1,4-Dichlorobutane
0.775
0.348
626
1,1,2,2-Tetrachloroethane
5.214
0.34
6179
Miscellaneous liquids Methyl acetate
0.494
0.341
370
Ethyl acetate
0.509
0.422
513
Ethyl benzoate
0.907
0.34
1111
Vasiliy V. Tereshatov and Valery Yu. Senichev
325
Table 6.4.1. Characteristics of polyurethane-solvent systems at 25oC. [Adapted, by permission, from U.S. Aithal, T.M. Aminabhavi, R.H. Balundgi, and S.S. Shukla, JMS - Rev. Macromol. Chem. Phys., 30C (1), 43 (1990).] Qmax
1
Mc
Methyl ethyl ketone
1.261
0.364
2088
Tetrahydrofuran
2.915
0.39
2890
Penetrant
1,4-Dioxane
2.267
0.376
2966
DMF
1.687
1.093
-1184
DMSO
0.890
1.034
-975
Acetonitrile
0.184
0.772
182
Nitromethane
0.302
1.160
5737
Nitroethane
0.463
0.578
382
n-Hexane
0.069
1.62
2192
Cyclohexane
0.176
0.753
287
Benzyl alcohol
4.221
In the second variant of evaluation of Mc, data on the temperature dependence of volume fraction of polymer, 2, in the swollen gel were used. Results of calculations of Mc from the Flory-Rehner equation in some cases also gave negative values. The evaluation of Mc in the framework of this approach is not an independent way, and Mc is an adjustment parameter, as is the parameter 1 of interaction between solvent and polymer. Previous evaluation of the physical network density of SPU was done on samples swollen to equilibrium in two solvents.2,9,10 Swelling of SPU in toluene practically does not affect hard domains.9,11 Swelling of SPU (based on oligoether diol) in a tributyl phosphate (a strong acceptor of protons) results in full destruction of the physical network with hard domains.2 The effective network density was evaluated for samples swollen to equilibrium in toluene according to the Cluff-Gladding method.12 Samples were swollen to equilibrium in TBP and the density of the physical network was determined from equation:2,10 v e V 0 dx – v e V 0 x = v e V 0 d
[6.4.2]
As the result of unequal influence of solvents on the physical network of SPU, the values of effective density of networks calculated for the “dry” cut sample can essentially differ. The examples of such influence of solvents are given in the work.2 SPU samples with oligodiene soft segments and various concentration of urethane-urea hard blocks were swollen to equilibrium in toluene, methyl ethyl ketone (MEK), tetrahydrofuran (THF), 1,4-dioxane and TBP (experiments 1-6, 9, 10, 12). SPU based on oligoether (experiment 7), with urethane-urea hard segments, and crosslinked single-phase polyurethanes (PU) on the base of oligodiene prepolymer with functional isocyanate groups, cured by oligoether triols (experiments 8, 11) were also used. The effective network densities of materials swollen in these solvents were evaluated by the Cluff-Gladding method
326
6.4 Influence of structure on equilibrium swelling
through the elasticity equilibrium modulus. The data are given in Table 6.4.2 per unit of initial volume. Table 6.4.2. Results of the evaluation of equilibrium swelling and network parameters of PUE. [Adapted, by permission, from E.N. Tereshatova, V.V. Tereshatov, V.P. Begishev, and M.A. Makarova, Vysokomol. Soed., 34B, 22 (1992).] #
kg/m3
Qv
ve/V0
Toluene
Qv
ve/V0 THF
Qv
ve/V0
MEK
Qv
ve/V0
Qv
1,4-Dioxane
ve/V0 TBP
1
996
1.56
1.03
0.46
0.77
1.08
0.41
3.76
0.12
5.12
0.06
2
986
2.09
0.53
0.52
0.43
1.40
0.23
6.22
0.04
11.15
0.02
0.73
0.01
3
999
1.74
0.77
0.49
4
1001
2.41
0.44
0.49
5
1003
4.46
0.15
0.47
6
984
2.63
0.40
0.57
1.11
0.38
7.88
0.03
18.48
1.75
0.13
14.3
0.02
0.19
3.44
0.14
4.21
3.29
0.39
1.45 1.40
0.73
1.86
0.31
7.22
0.04
1.01
0.54
2.08
0.34
1.48
0.35
7
1140
0.86
1.83
2.06
8
972
2.42
0.35
1.84
0.36
9
979
2.26
0.39
1.72
0.37
10
990
2.00
0.63
0.47
0.08
0.98
0.54
1.97
0.35
1.62
0.31
0.99
0.55
2.42
0.29
2.19
0.24
11
991
4.11
0.18
2.79
0.18
3.98
0.17
3.42
0.18
2.54
0.17
12
997
2.42
0.50
1.00
0.32
2.68
0.12
4.06
0.13
4.32
0.08
(ve/V0), kmol/m3
The data shows that the lowest values of the network density are obtained for samples swollen to equilibrium in TBP. Only TBP completely breaks down domains of hard blocks. If solvents, which are acceptors of protons (MEK, THF, 1,4-dioxane), are used in swelling experiment an intermediate values are obtained between those for toluene and TBP. The network densities of SPU (experiments 8 and 11) obtained for samples swollen in toluene, TBP, 1,4-dioxane and THF coincide (Table 6.4.2).2 To understand the restrictions to swelling of SPU caused by the physical network containing hard domains, the following experiments were carried out. Segmented polybutadiene urethane urea (PBUU) on the base of oligobutadiene diol urethane prepolymer with functional NCO-groups (M 2400 ), cured with MOCA, and SPU-10 based on prepolymer cured with the mixture of MOCA and oligopropylene triol (M 5000 ) were used. The chemical network densities of PBUU and SPU were 0.05 and 0.08 kmol/m3, respectively. The physical network density of initial sample, (ve/V0)d, of PBUU was 0.99 kmol/m3 and of SPU-10 was 0.43 kmol/m3. Samples of PBUU and SPU-10 were swollen to equilibrium in solvents of different polarity: dioctyl sebacate (DOS), dioctyl adipate (DOA), dihexyl phthalate (DHP), trans-
Vasiliy V. Tereshatov and Valery Yu. Senichev
327
former oil (TM), nitrile of oleic acid (NOA), dibutyl carbitol formal (DBCF), and tributyl phosphate (TBP). The values of equilibrium swelling of elastomers in these solvents, Q1, (ratio of the solvent mass to the mass of the unswollen sample) are given in Table 6.4.3. After swelling in a given solvent, samples were swollen in toluene to equilibrium. The obtained data for T swelling in toluene, Q V , indicate that the physical networks of PBUU and SPU-10 do not change on swelling in most solvents. Equilibrium swelling in toluene of initial sample and the sample previously swollen in other solvents is practically identical. Several other observations were made from swelling experiments, including sequential application of different solvents. If preliminary disruption of the physical network of PBUU and SPU-10 by TBP occurs, swelling of these materials in toluene strongly increases. Similarly, samples previously swollen in TBP have higher equilibrium swelling, Q2, when swollen in other solvents. The value of Q2 is likely higher than equilibrium swelling Q1 of initial sample (Table 6.4.3). Q2 for PBUU is closer to the value of equilibrium swelling of a single-phase crosslinked polybutadiene urethane, PBU, having chemical network density, (ve/V0)x = 0.04 kmol/m3. Thus, the dense physical network of polyurethane essentially limits the extent of equilibrium swelling in solvents, which does not breakdown the domain structure of a material. Table 6.4.3. Equilibrium swelling of SPBUU and SPU-10 (the initial sample and sample after breakdown of hard domains by TBP) and swelling of amorphous PBU at 25oC SPBUU Solvent
Initial structure Q1
-
QT
SPU-10
After breakdown of domains
Initial structure
Q2
Q1
1.35
After breakdown of domains
PBU
Q2
Q3 5.56
QT 2.10
DOS
0.62
1.34
3.97
0.66
2.09
3.04
DOA
0.68
1.34
4.18
0.84
2.05
3.26
DBP
0.60
1.36
3.24
0.90
2.12
3.38
DHP
0.63
1.34
3.71
0.85
2.10
3.22
4.47
TO
0.57
1.35
2.29
0.58
2.07
1.92
1.99
NOA
0.59
1.36
4.03
0.72
2.10
2.86
4.66
DBCP
0.69
1.37
4.60
0.155
2.96
3.45
5.08
TBP
5.01
7.92*
5.01
4.22
5.43
4.22
* The result refers to the elastomer, having physical network completely disrupted
Swelling of SPU can be influenced by changes in elastomer structure resulting from mechanical action. At higher tensile strains of SPU, a successive breakdown of hard domains as well as micro-segregation may come into play causing reorganization.13-15 If
328
6.4 Influence of structure on equilibrium swelling
the structural changes in segmented elastomers are accompanied by breakdown of hard domains and a concomitant transformation of a certain amount of hard segments into a soft polymeric matrix or pulling of some soft blocks (structural defects) out of the hard domains,14 variation of network parameters, is inevitable. It is known4 that high strains applied to SPU causes disruption of the physical network and a significant drop in its density. Table 6.4.4. Equilibrium swelling of SPU-1 samples in various solvents before and after stretching at 25oC (calculated and experimental data). [Adapted, by permission, from V.V. Tereshatov, Vysokomol. soed., 37A, 1529 (1995).] Solvent
1 kg/m3
V1×103 m3/kmol
Qv (=0)
1 (=0)
Qv (=700%) calc
exp
T
QV
(=700%)
T
QV
(=0)
Toluene
862
107
3.54
0.32
5.06
4.87
DBP
1043
266
1.12
0.56
1.47
1.53
4.85
3.49
n-Octane
698
164
0.79
0.75
0.90
0.93
4.94
3.60
Cyclohexane
774
109
1.46
0.60
1.78
1.95
4.99
3.63
p-Xylene
858
124
2.94
0.36
4.17
3.93
4.81
3.52
Butyl acetate
876
133
2.28
0.44
3.13
2.97
5.12
3.69
DOS
912
468
1.21
0.38
1.60
1.71
5.10
3.63
DOA
924
402
1.49
0.32
2.19
2.18
5.00
3.61
DHS
923
340
1.74
0.30
2.55
2.44
5.01
3.59
DHP
1001
334
1.25
0.47
1.71
1.74
4.79
3.47
DBCP
976
347
4.48
4.51
9.92
9.98
The data on equilibrium swelling of SPU-1 with oligodiene soft segments obtained by curing prepolymer by the mixture of MOCA and oligobutadiene diol (M 2000 ) with the molar ratio 1/1 are given in Table 6.4.4. The initial density of the SPU-1 network v e V 0 dx = 0.206 kmol/m3, the physical network density v e V 0 d = 0.170 kmol/ m3. After stretching by 700% and subsequent unloading, the value v e V 0 dx = 0.115 kmol/m3 and v e V 0 d = 0.079 kmol/m3. The density of the chemical network v e V 0 x = 0.036 kmol/m3 did not change. Samples were swollen to equilibrium in a set of solvents: toluene, n-octane, cyclohexane, p-xylene, butyl acetate, DBCF, DBP, DHP, dihexyl sebacate (DHS), DOA and DOS (the values of density, 1, and molar volume of solvents, V1, are given in Table 6.2.5). The data in Table 6.4.4 shows that, after stretching, the volume equilibrium swelling of samples does not change in DBCF.4 In other solvents equilibrium swelling is noticeably increased. Swelling experiments of samples previously swollen in solvents and subsequently in toluene have shown that the value of equilibrium swelling in toluene varies only for samples previously swollen in DBCF. The effective network densities evaluated for SPU-1 samples, swollen in DBCF, and then in toluene, have appeared equal (0.036 and 0.037
Vasiliy V. Tereshatov and Valery Yu. Senichev
329
kmol/m3, respectively) and these values correspond to the value of the chemical network parameter, (ve/V0)x, of SPU-1. It means that DBCF breaks down the physical network of elastomer; thus, the values of Qv in DBCF do not depend on the tensile strain. In all other cases, swelling of SPU-1 in toluene differs only marginally from the initial swelling of respective samples in toluene alone. Therefore, these solvents are unable to cause the breakdown of the physical network. The calculation of equilibrium swelling of SPU-1 (after its deformation up to 700% and subsequent unloading) in a given solvent was carried out using the Flory-Rehner equation. In our calculations we used values of the 1 parameter of interaction between solvents and elastomer calculated from experimental data of equilibrium swelling of initial sample ( = 0) in these solvents. The difference between calculated and experimental data on equilibrium swelling of SPU-1 samples after their deformation does not exceed 9%. Therefore, the increase in swelling of SPU-1 is not related to the change in the 1 parameter but it is related to a decrease in the (ve/V0)dx value of its three-dimensional network, caused by restructure of material by effect of strain. The change of the domain structure of SPU exposed to increased temperature (~200oC) and consequent storage of an elastomer at room temperature may also cause a change in equilibrium swelling of material.16 REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
V.P. Begishev, V.V. Tereshatov, E.N. Tereshatova, Int. Conf. Polymers in extreme environments, Nottingham, July 9-10, 1991, Univ. Press, Nottingham, 1991, pp. 1-6. E.N. Tereshatova, V.V. Tereshatov, V.P. Begishev, and M.A. Makarova, Vysokomol. Soed., 34B, 22 (1992). V.V. Tereshatov, E.N. Tereshatova, V.P. Begishev, V.I. Karmanov, and I.V. Baranets, Polym. Sci., 36A, 1680 (1994). V.V. Tereshatov, Vysokomol. soed., 37A, 1529 (1995). U.S. Aithal, T.M. Aminabhavi, R.H. Balundgi, and S.S. Shukla, JMS-Rev. Macromol. Chem. Phys., 30C (1), 43 (1990). P.J. Flory, Principles of Polymer Chemistry, Cornell Univ. Press, Ithaca, 1953. G.M. Bristow, and W.F. Watson, Trans. Faraday. Soc., 54, 1731 (1958). L.N. Mizerovsky, L.N. Vasnyatskaya, and G.M. Smurova, Vysokomol. Soed., 29A, 1512 (1987). D. Cohen, A. Siegman, and M. Narcis, Polym. Eng. Sci., 27, 286 (1987). E. Konton, G. Spathis, M. Niaounakis and V. Kefals, Colloid Polym. Sci., 26B, 636 (1990). V.V. Tereshatov, E.N. Tereshatova, and E.R. Volkova, Polym. Sci., 37A, 1157 (1995). E.E. Cluff, E.K. Gladding, and R. Pariser, J. Polym. Sci., 45, 341 (1960). Yu.Yu. Kercha, Z.V. Onishchenko, I.S. Kutyanina, and L.A. Shelkovnikova, Structural and Chemical Modification of Elastomers, Naukova Dumka, Kiev, 1989. Yu.Yu. Kercha, Physical Chemistry of Polyurethanes, Naukova Dumka, Kiev, 1979. V.N. Vatulev, S.V. Laptii, and Yu.Yu. Kercha, Infrared Spectra and Structure of Polyurethanes, Naukova Dumka, Kiev, 1987. S.V. Tereshatov, Yu.S. Klachkin, and E.N. Tereshatova, Plastmassy, 7, 43 (1998).
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6.5 EFFECT OF STRAIN ON THE SWELLING OF NANO-STRUCTURED ELASTOMERS Vasiliy V. Tereshatov, Vladimir N. Strelnikov, and Marina A. Makarova Institute of Technical Chemistry, Ural Branch of Russia Academy of Sciences, Perm, Russia Nano-heterogeneous elastomers with alternating soft and hard segments are used widely as compared with other block-copolymers having H-bonds. These are, for example segmented polyurethane ureas, SPUU, segmented polyurethanes, SPU, elastomers on the base of oligodiene urethane epoxides and so on.1-3 A significant difference in polarity leads to the microphase segregation of hard and soft segments with formation of hard segments' domains. These domains with sizes of 5-50 nm play a role of reinforcing fillers and crosslinking points of specific physical networks stable at elevated temperatures.1,4 Various combinations of physical-chemical and physical-mechanical properties of segmented elastomers, SE, can be achieved by changing the chemical structure of oligomers having terminated functional groups, diisocyanates, and low-molecular-mass chain extenders. It was determined that a dense physical network having crosslinking points forming hard domains is characteristic of segmented polyurethane ureas. This physical network limits swelling of SPUU in organic liquids that cannot dissolve hard domains. Exploitation of elastic products made from SE can be associated with appearing of great local deformations for example during periodical loading. Structure of these polymers can change at high deformations; domains of hard blocks are partially destroyed with formation of smaller domains; primary orientation takes place not only for soft segments, but for hard segments as well. Some hard segments are drawn out from some domains.5-9 As a result the density of physical network having crosslinking points forming hard domains can change. Sorption properties of a material in contact with low-molecular liquids can also change. This subchapter is devoted to the effect of strain on the sorption of organic solvents (plasticizers) by SE with various chemical and supramolecular structure. The sorption of liquids was compared before strain and after strain up to fixed values. The change in molecular and supramolecular structure of SPUU samples with soft segments of different polarity was investigated by the FTIR-spectroscopy method. It was made for the clarification of reasons of the effect of preliminary strain on the sorption of low-molecular-mass liquids, and for analysis of obtained results. Polyether urethane urea SPUU-T with polytetramethylene oxide soft segments (average molecular mass of soft segments M n =1430 g mol-1), polybutadiene urethane urea SPUU-D(M n = 2100 g mol-1), and polyurethane urea SPUU-TD with mixed polybutadiene and polytetramethylene oxide soft segments were investigated. The quantity of polar and non-polar soft segments was uniform for SPUU-TD. Materials were manufactured using a two stage technology. The first stage was reaction of 2,4-toluenediisocyanate and oligodiols: oligobutadienediol OBD (M n = 2100 g mol-1) and oligotetramethylene oxide diol OTM (M n = 1430 g mol-1). The ratio NCO/OH
332
6.5 Effect of strain on the swelling of nano-structured elastomers
was 2.03 at this stage. Prepolymers were cured at the second stage by methylene-bisortho-chloroaniline, MOCA, at 90oC for 3 days. The completeness of conversion of NCOgroups was controlled by the FTIR-spectroscopy. The methods of samples manufacturing are given elsewhere.10 Also, single-phase polyurethane PUE-TL was synthesized for comparison of sorption properties of this material and nano-heterogeneous SPUU. PUE-TL was synthesized on the base of prepolymer of OTM cured by mixture of the initial OTM and oligopropylene oxide triol Laprol 373 (M n = 370 g mol-1). FTIR-spectra of samples' surfaces were registered by the multiple attenuated total reflectance (MATR) method using the IFA-66/S spectrometer and specially designed MATR accessories with 45o KRS-5 trapezoid as the internal reflection element (operating number of reflections 1000). Tests were conducted using samples cut according to crystal size 20 40 mm2, thickness 2 mm before and after stretching up to the given strain value. The 20 80 mm2 sheets were stretched, then samples for spectra registration were cut off from working parts of sheets. The density of samples was determined by the hydrostatic method using AR-240 balance (Ohaus, Switzerland) with accuracy 2x10-7 kg. The density of physical network, which crosslinking points are hard domains, and the density of chemical network with chemical crosslinking points, was determined for SPUU using an approach developed by the authors.11 The total network density Ndx was determined using the compression modulus of samples swollen in toluene. Swelling in this solvent doesn't affect hard domains. The chemical network density Nx was determined testing samples swollen in tributyl phosphate. The physical network density was determined using difference Ndx Nx = Nd. For single-phase polyurethane Ndx = Nx (Nd = 0). Low-molecular-mass liquids, such as di-2(ethylhexyl) phthalate, DEHP, and liquid chlorinated paraffin HP-470 (M n =470 g mol-1) were used to investigate the strain effect on the sorption properties of SE and single-phase elastomer with a similar structure. Parts of samples were preliminary drawn up to 350%. Cylindrical specimens (5 mm diameter, 2 mm thickness) cut from drawn samples were immersed in the above mentioned liquids up to achievement of the constant mass at the temperature 25±1oC. Parts of non-drawn samples were immersed in these liquids up to equilibrium as well. The equilibrium swelling Q, wt%, and equilibrium concentration Cp, wt%, at swelling were determined. Q = 100m1/m0 where: m1 m0
mass of absorbed liquid initial mass of sample
Cp = 100m1/(m1 + m0) Table 6.5.1 contains data values for Q, Cp for three heterogeneous elastomers with urethane urea hard segments and a single-phase polyurethane PUE-TL. It is seen that preliminary strain = 350% does not practically affect the equilibrium swelling and the equilibrium concentration of this material at swelling in DEHP and HP-470.
Vasiliy V. Tereshatov, Vladimir N. Strelnikov, and Marina A. Makarova
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Table 6.5.1. Swelling data for SPUU and PUE-TL samples in DEHP and HP-470. DEHP Sample
= 0%
HP-470 = 350%
= 0%
= 350%
Q, wt% Cp, wt% Q, wt% Cp, wt% Q, wt% Cp, wt% Q, wt% Cp, wt% SPUU-D
62.6
38.5
70.1
41.2
47.5
32.2
53.8
35.0
SPUU-TD
40.6
28.9
53.8
35.0
44.3
30.7
58.7
37.0
SPUU-T
28.4
22.1
40.8
29.0
40.6
28.9
61.2
38.0
PUE-TL
187
65.2
186
65.0
154
60.6
156
60.9
Figure 6.5.1. FTIR-MATR spectra of SPUU-D (a), SPUU-T (b), and SPUU-TD(c).
The effect of strain differs significantly for swelling of SE with non-polar soft segments (SPUU-D) and ones with polar polyether segments (SPUU-T). Intermediate position in swelling value belongs to SPUU-TD with mixed soft segments. Preliminary strain affects equilibrium swelling of SPUU-D only a little. The values Q, and Cp for SPUU-T change significantly after strain.
334
6.5 Effect of strain on the swelling of nano-structured elastomers
The reason for this effect can be found out from the qualitative analysis of FTIR MATR spectra for SPUU-D, SPUU-TD, SPUU-T before and after strain up to 350%. (Figure 6.5.1). It is seen that integral spectral curve changes little after strain of SPUU-D with non-polar soft segments (Figure 6.5.1a). The band intensity of carbonyl at 1640 cm-1 decreases only a little after strain. This band refers to the absorption of hydrogen-bonded, ordered urea carbonyl. Urea groups are usually linked mutually (self-associates of urea groups) and localized in domains of the hard segments. The intensity of this band can be used for comparison of the microphase segregation degree for soft and hard segments.6 It is suggested that the band at 1663 cm-1 (1663-1666 cm-1) refers to the absorption of hydrogen-bonded, disordered urea carbonyls in the soft phase of polymer. The intensity of this band also changes little after the strain of SPUU-D (Figure 6.5.1a). Significant changes in the SPUU-T spectrum are seen after strain up to 350% (Figure 6.5.1b). The intensity of the band at 1642 cm-1 decreases significantly (the band of carbonyl absorption shifts by 2 cm-1 to the side of higher values of the wave number), that shows decreasing in the degree of microphase segregation of hard and soft segments. The concentration of hard phase in a material decreases as well. The intensity of band at 1729 cm-1 for free urethane carbonyl and band at 1711 cm-1 for hydrogen-bonded, disordered urea carbonyl in the soft phase of polymer increases. Thus, redistribution of intensity of carbonyl absorbance in hard and soft phase of polyurethane urea is seen. The assignment of carbonyl bands is based on results published elsewhere.12-15 The degree of microphase segregation of hard and soft segments in SPUU-TD decreases less than in SPUU-T, but more than in SPUU-D (Figure 6.5.1c). The results of the analysis of FTIR MATR spectra and data for change in physical network density (for network with hard domains playing a role of crosslinking points) after strain of investigated materials correlate (Table 6.5.2). The value Nd for physical network decreases from 1.42 to 1.1 kmol/m3 for SPUU-T, from 1.09 to 0.88 kmol/m3 for SPUU-TD, from 0.78 to 0.68 kmol/m3 for SPUU-D. The data permit to explain differences in sorption values for SPUU after strain. Table 6.5.2. Network parameters for SPUU and single-phase polyurethane PUE-TL before strain and after strain up to 350% N, kmol/m3 Material
, kg/m3
Ndx
Nx
Mdx, kg/kmol
Nd
0
350%
0
350%
0
350%
0
350%
SPUU-T
1100
1.42
1.10
0.04
0.04
1.38
1.06
770
1000
SPUU-TD
1041
1.09
0.88
0.04
0.04
1.05
0.84
955
1180
SPUU-D
989
0.78
0.68
0.05
0.05
0.73
0.63
1270
1450
PUE-TL
1056
0.14
0.14
0.14
0.14
0
0
7600
7600
The decrease in the Nd value (for physical network) and data on the spectral analysis show the partial rupture of hard domains. A part of hard segments transfers to the soft
Vasiliy V. Tereshatov, Vladimir N. Strelnikov, and Marina A. Makarova
335
phase after straining. As a result the volume of polymer available for plasticizer molecules increases. Therefore, two factors promote the increase of solubility of SPUU in liquids: decrease in the physical network density and the increase in the volume fraction of soft phase in heterogeneous polymer.These factors affect swelling of SPUU-TD with polyether soft segments to higher degree after straining. The equilibrium swelling Q and concentration of liquid in SPUU change after strain less in the case when some soft polyether segments are replaced by polydiene segments. Lower rupture of hard domains leads to the little change in swelling values for polydieneurethane urea in DEHP and HP-470. An effect of strain on swelling of segmented polyurethane SPU and three polyurethane ureas SPUU-TD, SPUU-1, and SPUU-P was investigated for 11 polar and non-polar solvents (plasticizers). Molecular mass of polytetramethylene oxide soft segments and polypropylene oxide soft segments (Mn) is 1000 g mol-1 in SPUU-1. Polyurethane was synthesized via curing of prepolymer OTM (M n = 2000 g mol-1) by BD. Synthesis of prepolymer was conducted using diphenylmethane diisocyanate, MDI. The molar ratio NCO/ OH = 0.98. The molar ratio OTM/MDI = 2.2. The methods of sample manufacture are given elsewhere.10 The values of an effective network density Nd for SPU, SPUU-TD, SPUU-1, and SPUU-P are 0.56, 1.05, 1.75, 1.30 kmol/m3, respectively. Samples were swollen at 25±1oC before the strain and after strain up to the value 350% in the following liquids: ethyl acetate, n-octane, p-xylene, toluene, butyl acetate, isoamyl alcohol, DEHP, dibutyl phthalate, DBP, dibutyl sebacate, DBS, di-(2-ethylhexyl) sebacate, DEHS, and tributyl phosphate, TBP. The results show that samples of linear SE are completely solvable in TBP which is a strong acceptor of protons independent of the structure and polarity of soft segments. The physical network with crosslinking points which are hard domains limits equilibrium swelling in many solvents. This is clearly seen from an example of SPUU-1 with high effective density of such network Ndx = 1.75 kmol/m3. The Q value in the majority of solvents is below 50% (Table 6.5.3). The maximal sorption was obtained for segmented polyurethane with lower physical network density. Preliminary strain leads to increase in plasticizer sorption. Thus, determined peculiarities are characteristic for segmented heterogeneous elastomers with urethane urea and urethane hard segments. It is interesting to note that strain affects the swelling of SE in many liquids with the less degree in the case of low network density Nd value. This is evidently seen for example of SPU. Table 6.5.3. Equilibrium swelling of segmented polyurethane and polyurethane ureas in solvents (plasticizers). Solvent (plasticizer)
Q, % ( = 0)
Q, % ( = 350)
SPUU-TD
SPUU-1
SPU
SPUU-P
SPUU-TD
SPUU-1
SPU
SPUU-P
Ethyl acetate
64
45
120
116
78
60
133
132
Octane
22
6
15
7
28
7
19
8
p-Xylene
89
48
128
14
6
146
336
6.5 Effect of strain on the swelling of nano-structured elastomers
Table 6.5.3. Equilibrium swelling of segmented polyurethane and polyurethane ureas in solvents (plasticizers). Solvent (plasticizer)
Q, % ( = 0)
Q, % ( = 350)
SPUU-TD
SPUU-1
SPU
SPUU-P
SPUU-TD
SPUU-1
SPU
SPUU-P
Toluene
106
57
158
74
130
78
174
86
Butyl acetate
71
44
135
94
89
62
142
109
Isoamyl alcohol
24
29
70
28
38
73
DEHP
41
15
72
7
54
24
77
10
BBP
48
35
41
63
53
58
DBS
48
26
95
38
65
40
99
48
DEHS
29
10
41
39
14
43
TBP
872
878
CONCLUSIONS The effect of preliminary strain on the sorption of liquids of various chemical structure by segmented polyurethane and polyurethane ureas was investigated. It was shown that the swelling degree increases after strain as a result of partial destruction of domain structure and decrease in effective density of the physical network formed by hard domains. It was determined that increase in destruction of domain structure of a material leads to further change in solubility of liquids in an elastomer. This effect is less pronounced in low dense networks and disappears at all in the case of absence of such network (for single-phase elastomers). However in this last case effect of limiting swelling in various liquids due the presence of physical network stable to the solvent action decreases, or disappears. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Z.S. Petrovic, J.Ferguson, J. Polym. Sci., 16, 695 (1991). D. Randall, S. Lee, The polyurethanes book. Wiley, New York, 2003. T. Thomson, Polyurethanes as specialty chemicals: principles and applications, CRC Press, Boca Raton, 2005. V. V.Tereshatov, V. N.Strel'nikov, M. A. Makarova, V. Yu. Senichev, and E. R.Volkova, Russ. J. Appl. Chem., 83, 1380 (2010). F. Yeh, B.S. Hsiao, B.B. Sauer, S. Michel, H.W. Siesler, Macromolecules, 36, 1940 (2003). E.M. Christenson, J.M. Anderson, A. Hiltner, E. Baer, Polymer, 46, 1744 (2005). G. Muller-Riederer, R. Bonart, Progr. Colloid. Polym. Sci., 62, 99 (1977). R. Bonart, K. Hoffman, Colloid Polym. Sci., 260, 268 (1982). V.V. Tereshatov, Polym. Sci., 37, 946 (1995). V.V. Tereshatov, M.A. Makarova, V.Yu. Senichev, A.I. Slobodinyuk, Colloid Polym. Sci., 290, 641 (2012). V.V. Tereshatov, E.N. Tereshatova, E.R.Volkova, Polym. Sci., 37, 1157 (1995). R.W. Seymor, G.M. Estes, S.L. Cooper, Macromolecules, 3, 579 (1970). L. Ning, W. De-Nung, Y. Sheng-Kang, Macromolecules, 30, 4405 (1997). V.V. Tereshatov, M.A. Makarova, E.N. Tereshatova, Polym. Sci. A., 46, 1332 (2004). C.M. Brunette, S.L. Hsu, W.J. MacKnight, Macromolecules, 15, 71 (1982).
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6.6 THE EFFECT OF THERMODYNAMIC PARAMETERS OF POLYMERSOLVENT SYSTEM ON THE SWELLING KINETICS OF CROSSLINKED ELASTOMERS Vasiliy V. Tereshatov, Elena R. Volkova, Evgeniy Ya. Denisyuk, and Vladimir N. Strelnikov Institute of Technical Chemistry Ural Branch of Russian Academy of Sciences, Perm, Russia Swelling of polymeric materials is a special case of mechanic-diffusion processes, i.e. cooccurring and interrelated processes of the fluid diffusion and strain of a material. Threedimensional non-linear theory1 of such processes was used to study swelling of elastomeric polymer networks in low-molecular solvents elsewhere.2,3 A mathematical model describing the non-equilibrium swelling process flowing at finite strains was developed for a flat elastomer sample or a polymer gel.2 Regularities of non-equilibrium processes of polymer networks swelling were described at very low swelling degrees4-6 and at high swelling degrees.2-4 However, the actual swelling process is accompanied usually by a finite strain of a material, the amount of which is determined by the quality of a solvent and varies widely. This subchapter presents the results of theoretical and experimental studies on the influence of solvent properties on the nature of the swelling kinetics for elastomeric polymer networks at finite strains of the polymer matrix. Emphasis is focused on the study of the relationship of the asymptotic properties of the swelling kinetic curves with the thermodynamic quality of a solvent. The chemical potential of a solvent in the sample under swelling is given by the following equation:2 2
–1 4 3 –1 –4
= RT ln 1 – + + + Z E where:
V1, V2 Z = V2/V1 E =
[6.6.1]
Flory-Huggins parameter molar volumes of a solvent and the same for subchains of polymer network dimensionless parameter local volume fraction of a polymer in the swollen sample volume fraction of a polymer in the swollen material at equilibrium longitudinal elongation of the sample under swelling.
Equation [6.6.1] is written in the reference configuration. This configuration corresponds to the state of a material at equilibrium swelling. This means that = 1 in this state, 13 and = E for the initial (unswollen) state. For this reason, h is one half of the sample thickness in the equilibrium swollen state. The reference state is the state of the material, which is considered as unstrained; thereafter a strain is determined with respect to it. In the case of swellable materials any state of undistorted material, in which solvent is distributed uniformly over its volume, can be used as a reference configuration.1,2 Equation [6.6.1] describes the dependence of the chemical potential of a solvent absorbed by the sample under symmetrical biaxial stretching and compression. Equating it
338
6.6 The effect of thermodynamic parameters of polymer-solvent system
to zero, we obtain an equation that can be used to calculate the equilibrium swelling 13 degree of a sample under these conditions. In particular, if = E , we obtain the following equation 2
–1 –1
ln 1 – + + + Z
= 0
[6.6.2]
which determines the local swelling degree on the sample surface during the time of immersion in the solvent. When = 1, we obtain the well-known Flory-Rehner equation 2
–1 1 3
ln 1 – E + E + E + Z E
= 0
[6.6.3]
The kinetic curve is an integral characteristic of the swelling process g = u x
[6.6.4]
which is usually determined by swelling experiments.7 The diffusion kinetics of flat sample swelling depends on the parameters and Z. Flory-Huggins parameter is a quantitative measure of the thermodynamic quality of a solvent for the given polymer. For good solvents < 0.5, and for the bad ones > 0.5. The value of = 0.5 corresponds to the so-called -solvents. As is shown below, the value determines largely the swelling kinetics. The value of Z affects the equilibrium swelling degree of the material. Next, we consider the elastomeric polymer networks and low-molecular-weight solvents for which Z >> 1. The initial part of the kinetic curve is described by the following equation:8 g = M
q
[6.6.5]
Curves of distribution of diffusing liquid on the sample thickness are presented for various times (dimensionless) in the earlier reference.8 = tD/h2, where t swelling time (with dimension); D diffusion coefficient; h one half of the sample thickness. Figure 6.6.1 shows that dimensionless boundary concentration of solvent u1 differs significantly from 1 for a good solvent ( < 0.5) and for a -solvent ( = 0.5) as well. This means that the liquid concentration on the boundary of the sample-liquid contact at the initial swelling stage is significantly less than equilibrium value u = 1. In the case of a poor solvent u 1 1 . Swelling kinetic curves are described by the law of normal sorption ( > 0.5). When < 0.5 swelling curves are S-shaped ones. Kinetic curves of swelling of a sample in a good solvent shown in the coordinates ( ; g) are S shaped, and their initial region described by equation [6.6.1] with the parameter q > 0.5. Figures 6.6.1 and 6.6.2 show the results of numerical solution of the boundary problem for a variety of solutions of . One can see how the nature of the diffusion process and the shape of swelling kinetic curves changes depending on the deterioration of the thermodynamic quality of solvent. Particularly, it can be seen that as the parameter FloryHuggins increases the interval of the boundary concentration decreases, and swelling kinetic curves transform to kinetic curve of the normal sorption. The swelling kinetics of polydiene-urethane epoxide crosslinked elastomer (PDUE) was investigated for the experimental verification of the theoretical analysis. It was pro-
Vasiliy V. Tereshatov et al.
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Figure 6.6.1. Distribution of the fluid during diffusion at different time points = tD/h2 for swelling of a plane layer in a good solvent ( = 0), in a -solvent ( = 0.5), and in a poor solvent ( = 0.8) 1) = 0.01; 2) = 0.1; 3) = 0.2; 4) = 0.4; 5) = 0.6; 6) = 0.8; 7) = 1.0; 8) = 1.5. The curves were obtained at Z = V2/V1 = 200. [Adapted, by permission, from E.Ya. Denisyuk, E.R. Volkova, Vysokomolek. Soed., 45A, 1160 (2003).]
vided for solvents with different thermodynamic quality: dioctyl sebacate (DOS), dioctyl adipate (DOA), dibutyl sebacate (DBS), dioctyl phthalate (DOP), CCl4, toluene, dibutylcarbitolformal (DBKF), dimethyl adipate (DMA), and triacetin.8 PDUE elastomer was obtained by curing oligodiene (vinyl-isoprene) urethane epoxide (M = 5×103) by oligodivinyl carboxylate-terminated oligomer SKD-KTR (M = 3×103) at the molar ratio of 1:0.56. Samples of elastomers were cured for 4 days at 80°C.
340
6.6 The effect of thermodynamic parameters of polymer-solvent system
Figure 6.6.2. Theoretical kinetic curves for swelling of a flat layer at different values of the Flory-Huggins parameter and fixed value of Z = V2/V1 = 200: 1) = 0; 2) = 0.4; 3) = 0.5; 4) = 0.6; 5) = 1.0. [Adapted, by permission, from E.Ya. Denisyuk, E.R. Volkova, Vysokomolek. Soed., 45A, 1160 (2003).]
Figure 6.6.3. The experimental kinetic curves of PDUE samples swelling in solvents of different thermodynamic quality: DOS ( = 0), DOA ( = 0.02), DBS ( = 0.132), DBKF ( = 0.46), and DMA ( = 0.93).
Molar volume of the polymer network chains V2 was evaluated by the shear modulus G of a sample swollen in toluene up to equilibrium. The parameter value was estimated for each solvent using equation [6.6.3]. Kinetic curves of swelling were calculated according to the formula g(t) = m(t)/mE, where m(t), mE current value of the mass of a liquid absorbed by sample and finite one, respectively. Experiments were carried out by swelling at 25oC. Figure 6.6.3 shows the kinetic curves of the samples PDUE swelling in solvents of different thermodynamic quality. Table 6.6.1 shows the experimental values of the parameters characterizing the swelling kinetics. Table 6.6.1. Parameters of kinetic curves of swelling of PDUE elastomer in solvents of various thermodynamic quality. [Adapted, by permission, from E.Ya. Denisyuk, E.R.
Volkova, Vysokomolek. Soed., 45A, 1160 (2003)]. E
Z
u, %
q
qexp
Dx1011, m2/s
DOS
0.157
0.0
35
64
0.68
0.665
0.81
DOA
0.156
0.02
41
64
0.7
0.665
2.25
DBS
0.161
0.132
49
63
0.7
0.660
3.29
DOP
0.181
0.152
41
61
0.71
0.652
0.71
CCl4
0.0917
0.218
170
69
0.67
0.674
32.8
DBKF
0.291
0.460
47
47
0.58
0.603
1.89
DMA
0.654
0.930
94
4.2
0.52
0.506
2.26
Triacetin
0.943
2.1
87
0.14
0.50
0.500
0.24
Solvent
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It is seen from Figure 6.6.3 and Table 6.6.1 how the kinetic curves of elastomer swelling transform when the quality of the solvent decreases. For example, these curves are S-shaped ones for solvents with smaller than 0.5. This is evidenced by the fact that the parameter q > 0.5, and its value is close to the value of 0.7 corresponding to the limited self-similar regime of swelling of a material in good solvents at a constant diffusion coefficient. S-shape of the kinetic curve of swelling in DBKF is defined poorly, but its properties are close to -solvents. Kinetic curves of swelling in DMA, which is a poor solvent for a given polymer, have the shape characteristic for the kinetic curves of normal sorption. They have a distinct linear region, and the S-shape is absent. This corresponds to the value of q 0.5 . As previously shown,8 the determination of the diffusion coefficient D should be provided in analyzing the final section of the kinetic curve of swelling. This curve is described by the universal expression 2 –1
g t = 1 – C exp – 1 h Dt
[6.6.6]
where: g (t) t C h D 1
the ratio of the current mass value of an absorbed liquid to the equilibrium one time of swelling constant one half of the sample thickness in the reference configuration diffusion coefficient of a solvent in material. the first positive root of the equation n = tg n .
The value , taking into account the properties of a solvent, is determined using the following equation:8 4 1 – E = ---------------------------------------------------------------------------53 3 Z E 1 – 2 1 + 2 1 E + 1
[6.6.7]
In this case, the diffusion coefficient D includes physical parameters and geometric factors associated with the particular mode of the strain process of polymer matrix during swelling. In addition, it depends essentially on the choice of the reference state, which is necessary to fix the description of the swelling process. It was shown that such choice was ambiguous.2 Any undistorted state can be used as the reference state when material is not subjected to the mechanical stresses, and the fluid is uniformly distributed in volume. However, the situation is simpler in the case of materials with low swelling degree. Here geometric factors play a minor role and the size of the sample differs slightly in the “dry” state and in the swollen one. The diffusion coefficient D is weakly dependent on the choice of the reference state; it can be approximately regarded as a physical characteristic of the process. The efficiency of the theory is demonstrated for the single-phase crosslinked polyurethane elastomers. At low degrees of swelling of materials in liquids, equation [6.6.6] can be transformed with simplification into the expression:
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6.6 The effect of thermodynamic parameters of polymer-solvent system 2
kh D = -------21
[6.6.8]
where: h 1 2 k
one half of the sample thickness in the equilibrium swollen state for poor solvents and materials with low swelling degree2 slope coefficient, calculated on the final sections of the kinetic curves of swelling, plotted in coordinates (t;ln(1 g)).
Expression [6.6.8] describes the kinetics of the normal absorption of liquid in the presence of which the spatial polymer network remains unchanged (absence of chemical network destruction). In the case of micro-heterogeneous materials with block structure, such as segmented polyurethanes and polyurethane ureas, the absorption of the liquid should not lead to the chemical network destruction, and to the destruction of the physical network having crosslinking points forming hard domains. This subchapter presents the results of a study on the absorption kinetics of a number of liquids for segmented polyether urethane urea. Estimation of the diffusion coefficient of liquids was made for crosslinked polymers with a spatial network where crosslinking points are caused by chemical bonds and hard segment domains. The object of the study was a micro-heterogeneous polyurethane urea (PUU) based 3 on the prepolymer SKU-PFL-100 (M 1.4 10 ), synthesized by the interaction of oli3 gotetramethylene oxide diol (M 1 10 ) with a double excess of 2,4-toluene diisocyanate. MOCA (aromatic diamine: 3,3’-dichloro-4,4’-diaminodiphenyl methane) was used to cure SKU-PFL-100. The NCO/NH2 ratio was 1.2 for this reaction. Prepolymer was degassed at 50 10 oC before the reaction. Reaction mixture was stirred for 3 minutes at 50 1 oC and a residual pressure of 1-2 kPa after injection of melted aromatic diamine. Curing period was 3 days at 80 2 oC. Cured samples were further stored at the room temperature for at least 30 days. Sorption kinetics of elastomer was studied for following liquids: toluene, DBS, DOA, and transformer oil (TO). The study of the kinetics of swelling was conducted using samples manufactured in the form of discs of 35 mm in diameter and 2 mm in thickness. The kinetics of swelling was measured gravimetrically. A sample was immersed in a plasticizer and periodically weighed using analytical balance. The experiment time was determined via establishment of the equilibrium concentration of a solvent in sample. Experiments were carried out at 24 1 °C. Determination of spatial network parameters for elastomers was determined before achievement of the value of the equilibrium swelling of the elastomer in the liquid and after it. Total effective network density Ndx of chemical network and physical network of a polymer resulting from its domain structure, and the density of chemical network Nx were determined by the method described elsewhere.9 Properties of used liquids and the network parameters are shown in Table 6.6.2. Estimation of the network parameters for polymer network shows that the values Ndx and Nx remain almost unchanged before swelling of the polymer in organic liquids and after it. This, according to the previous study,10
Vasiliy V. Tereshatov et al.
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demonstrates the stability of not only chemical but also the physical network of the polymer to the action of the liquids. Based on the data on the total network density, Ndx, and equilibrium swelling of PUU according to the Flory-Rehner equation11 the estimation of the parameter (polymer-liquid interaction) was made for used liquids. Table 6.6.2. Properties of low-molecular-mass liquids and PUU samples swollen in them. [Adapted, by permission, from V.V. Tereshatov, E.R. Volkova, E.Ya. Denisyuk,
Plastmassy, 13, No.12, 14 (2004).] Solvent
Molar vol. V, cm3/mol
Eq. swelling Q, %
Network density, kmol/m3
1
kx102, s-1
Dx1012, m2/s
Ndx
Nx
1.67
0.22
TO
300
6.8
1.67
0.22
1.7
0.72
0.53
DOA
399
12.6
1.67
0.22
1.2
0.75
0.61
DBS
336
17.8
1.67
0.22
1.0
0.93
0.83
Toluene
106
46.8
1.67
0.22
0.7
47.1
43.0
Figure 6.6.4. Kinetic curves for swelling of PUU in toluene, DBS, DOA, and TO. [Adapted, by permission, from V.V. Tereshatov, E.R. Volkova, E.Ya. Denisyuk, Plastmassy, 13, No.12, 14 (2004).]
Figure 6.6.5. Dependences for calculation of k coefficient for the final stage of PUU swelling in toluene, DBS, DOA, and TO. [Adapted, by permission, from V.V. Tereshatov, E.R. Volkova, E.Ya. Denisyuk, Plastmassy, 13, No.12, 14 (2004).]
Figure 6.6.4 shows the results of a study of the kinetics of absorption of low-molecular-mass liquid by polymer. It can be seen that all swelling kinetic curves plotted in the coordinates ( t ; g), have an initial linear stage, i.e., kinetic curves are normal sorption ones. Consequently, the experimental values of the diffusion coefficient D, can be calculated using equation [6.6.8]. Figure 6.6.5 shows the swelling kinetic curves plotted in the coordinates (t;ln(1 g)). They take the shape of straight lines with a slope coefficient k at
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6.6 The effect of thermodynamic parameters of polymer-solvent system
g 0.4 . Diffusion coefficients for PUU and non-volatile liquids DBS, DOA, TO, and volatile solvent toluene were determined using obtained k values (Table 6.6.2). The results of calculations show that the diffusion coefficients of DBS, DOA, and TO in PUU differ only a little. The diffusion coefficient of toluene is many times higher due to the fact that its molar volume V1 is much smaller. Increase in D during swelling of polymer in toluene according to the previous data8 is also a natural consequence of the greater thermodynamic affinity for toluene to PUU comparing with other solvents. This can be seen from the values of parameter 1 shown in Table 6.6.2. Results of investigations show that the proposed approach is quite justified to describe the kinetics of swelling of segmented polyurethanes in low-molecular-mass liquids at a small value of the equilibrium swelling (Q 50 %) and in the case of the absence of significant effect of a solvent (or plasticizer) on the microphase segregation in the material. In this case, the law of normal sorption of a liquid by a crosslinked polymer is keep on. CONCLUSIONS 1. The effect of the thermodynamic quality of solvent on the swelling kinetics of elastomeric polymer networks was theoretically and experimentally studied. Swelling is considered as a set of interrelated processes of diffusion and strain of a material. It is shown that the quality of a solvent, estimated by the Flory-Huggins parameter value, significantly affects the nature of kinetic curves of polymer network swelling. 2. It was found that swelling curves are S-shaped ones for values of the Flory-Huggins parameter less than 0.5. Swelling is described by the law of normal sorption in poor solvents. 3. It was shown that the determination of the diffusion coefficient was to carry on the final stage of the swelling kinetic curve, which was described by a universal asymptotic expression [6.6.6]. The initial stage of the kinetic curve for this is of little use, because it is not possible to obtain a sufficiently accurate and simple analytical expression. 4. It was found that increase in solubility of a liquid in polymer had a positive effect on the diffusion coefficient of the solvent under swelling of crosslinked elastomer therein. REFERENCES 1. 2. 3. 4. 5. 6. 7.
E.Ya. Denisyuk, V.V. Tereshatov, Appl. Mechanics Techn. Phys., 38, 113 (1997). E.Ya. Denisyuk, V.V. Tereshatov, Vysokomolek. Soed., 42A, 71 (2000). E.Ya. Denisyuk, V.V. Tereshatov, Vysokomolek. Soed., 42A, 2130 (2000). T. Tanaka, D. Fillmore, J. Chem. Phys., 70, 1214 (1979). A. Peters, S.J. Candau, Macromolecules, 21, 2278 (1988). Y. Li, T. Tanaka, J. Chem. Phys., 92, 1365 (1990). A.Ya. Malkin, A.E. Chalykh, Diffusion and Viscosity of Polymers. Methods of determination (In Russian). Chemistry, Moscow, 1979. 8. E.Ya. Denisyuk, E.R. Volkova, Polym. Sci., 45A, 686 (2003). 9. E.N. Tereshatova, V.V. Tereshatov, V.P. Begishev, M.A. Makarova, Vysokomolek. Soed, 34B, 22(1992). 10. V.V. Tereshatov, V.Yu. Senichev, Influence of structure on equilibrium swelling. In Handbook of Plasticizers, ChemTec Publishing, Toronto, 2005. 11. P.J. Flory, Principles of Polymer Chemistry, Cornell Univ. Press, Ithaca, 1953. 12. V.V. Tereshatov, E.R. Volkova, E.Ya. Denisyuk, Plastmassy, 13, No.12, 14 (2004)